Stochastic models for fractional calculus /:
This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic lim...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin :
De Gruyter,
©2012.
|
| Schriftenreihe: | De Gruyter studies in mathematics ;
43. |
| Schlagworte: | |
| Online-Zugang: | Volltext Volltext |
| Zusammenfassung: | This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. |
| Beschreibung: | 1 online resource (x, 294 pages) : illustrations |
| Bibliographie: | Includes bibliographical references (pages 279-288), and index. |
| ISBN: | 9783110258165 3110258161 3110258692 9783110258691 9783110559149 3110559145 |
| ISSN: | 0179-0986 ; |
Internformat
MARC
| LEADER | 00000cam a2200000Mi 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn772845223 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr |n|---||||| | ||
| 008 | 120116s2012 gw a ob 001 0 eng d | ||
| 010 | |z 2011036413 | ||
| 040 | |a EBLCP |b eng |e pn |c EBLCP |d OCLCQ |d YDXCP |d N$T |d OCLCQ |d OCLCF |d DEBSZ |d OCLCQ |d OCLCO |d DEBBG |d E7B |d IDEBK |d OCLCQ |d COO |d OCLCQ |d UIU |d AGLDB |d AZK |d YDX |d MOR |d PIFAG |d ZCU |d OTZ |d OCLCQ |d MERUC |d OCLCQ |d DEGRU |d DKDLA |d OCLCQ |d VTS |d ICG |d OCLCQ |d STF |d LEAUB |d DKC |d AU@ |d OCLCQ |d UKAHL |d OCLCQ |d TXI |d U3W |d WRM |d INT |d VT2 |d WYU |d TKN |d HS0 |d OCLCQ |d VLY |d AUD |d AJS |d S2H |d OCLCO |d UKCRE |d OCLCO |d OCLCQ |d INARC |d OCLCO |d OCLCL |d OCLCQ | ||
| 019 | |a 785776485 |a 961527204 |a 979584734 |a 985273235 |a 985390879 |a 988416544 |a 988476448 |a 991924826 |a 994927097 |a 1013184144 |a 1018005982 |a 1037712939 |a 1038654813 |a 1038688029 |a 1055401727 |a 1058126024 |a 1059082058 |a 1064747765 |a 1081293925 |a 1096236715 |a 1119122738 |a 1152986076 |a 1162004094 |a 1264840415 |a 1290043454 |a 1300495312 |a 1388226056 |a 1392024835 | ||
| 020 | |a 9783110258165 |q (electronic bk.) | ||
| 020 | |a 3110258161 |q (electronic bk.) | ||
| 020 | |a 3110258692 | ||
| 020 | |a 9783110258691 | ||
| 020 | |a 9783110559149 |q (electronic bk.) | ||
| 020 | |a 3110559145 |q (electronic bk.) | ||
| 024 | 7 | |a 10.1515/9783110258165 |2 doi | |
| 035 | |a (OCoLC)772845223 |z (OCoLC)785776485 |z (OCoLC)961527204 |z (OCoLC)979584734 |z (OCoLC)985273235 |z (OCoLC)985390879 |z (OCoLC)988416544 |z (OCoLC)988476448 |z (OCoLC)991924826 |z (OCoLC)994927097 |z (OCoLC)1013184144 |z (OCoLC)1018005982 |z (OCoLC)1037712939 |z (OCoLC)1038654813 |z (OCoLC)1038688029 |z (OCoLC)1055401727 |z (OCoLC)1058126024 |z (OCoLC)1059082058 |z (OCoLC)1064747765 |z (OCoLC)1081293925 |z (OCoLC)1096236715 |z (OCoLC)1119122738 |z (OCoLC)1152986076 |z (OCoLC)1162004094 |z (OCoLC)1264840415 |z (OCoLC)1290043454 |z (OCoLC)1300495312 |z (OCoLC)1388226056 |z (OCoLC)1392024835 | ||
| 037 | |a 835465 |b Proquest Ebook Central | ||
| 050 | 4 | |a QA314 .M484 2011 | |
| 072 | 7 | |a MAT |x 005000 |2 bisacsh | |
| 072 | 7 | |a MAT |x 034000 |2 bisacsh | |
| 082 | 7 | |a 515.83 | |
| 084 | |a SK 950 |2 rvk | ||
| 084 | |a SK 820 |2 rvk |0 (DE-625)rvk/143258: | ||
| 049 | |a MAIN | ||
| 100 | 1 | |a Meerschaert, Mark M., |d 1955- |1 https://id.oclc.org/worldcat/entity/E39PBJvtdRBcfXWGf46Jc7dfbd |0 http://id.loc.gov/authorities/names/n92103385 | |
| 245 | 1 | 0 | |a Stochastic models for fractional calculus / |c Mark M. Meerschaert, Alla Sikorskii. |
| 260 | |a Berlin : |b De Gruyter, |c ©2012. | ||
| 300 | |a 1 online resource (x, 294 pages) : |b illustrations | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file |2 rda | ||
| 490 | 1 | |a De Gruyter studies in mathematics, |x 0179-0986 ; |v 43 | |
| 504 | |a Includes bibliographical references (pages 279-288), and index. | ||
| 505 | 0 | 0 | |t Introduction ; |t The traditional diffusion model -- |t Fractional diffusion -- |t Fractional derivatives ; |t The Grünwald formula -- |t More fractional derivatives -- |t The Caputo derivative -- |t Time-fractional diffusion -- |t Stable limit distributions ; |t Infinitely divisible laws -- |t Stable characteristic functions -- |t Semigroups -- |t Poisson approximation -- |t Shifted Poisson approximation -- |t Triangular arrays -- |t One-sided stable limits -- |t Two-sided stable limits -- |t Continuous time random walks ; |t Regular variation -- |t Stable central limit theorem -- |t Continuous time random walks -- |t Convergence in Skorokhod space -- |t CTRW governing equations -- |t Computations in R ; |t R codes for fractional diffusion -- |t Sample path simulations |
| 505 | 0 | 0 | |t Vector fractional diffusion ; |t Vector random walks -- |t Vector random walks with heavy tails -- |t Triangular arrays of random vectors -- |t Stable random vectors -- |t Vector fractional diffusion equation -- |t Operator stable laws -- |t Operator regular variation -- |t Generalized domains of attraction -- |t Applications and extensions ; |t LePage series representation -- |t Tempered stable laws -- |t Tempered fractional derivatives -- |t Pearson diffusions -- |t Fractional Pearson diffusions -- |t Fractional Brownian motion -- |t Fractional random fields -- |t Applications of fractional diffusion -- |t Applications of vector fractional diffusion. |
| 520 | |a This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a In English. | ||
| 650 | 0 | |a Fractional calculus. |0 http://id.loc.gov/authorities/subjects/sh93004015 | |
| 650 | 0 | |a Diffusion processes. |0 http://id.loc.gov/authorities/subjects/sh85037941 | |
| 650 | 0 | |a Stochastic analysis. |0 http://id.loc.gov/authorities/subjects/sh85128175 | |
| 650 | 6 | |a Dérivées fractionnaires. | |
| 650 | 6 | |a Processus de diffusion. | |
| 650 | 6 | |a Analyse stochastique. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Mathematical Analysis. |2 bisacsh | |
| 650 | 7 | |a Diffusion processes |2 fast | |
| 650 | 7 | |a Fractional calculus |2 fast | |
| 650 | 7 | |a Stochastic analysis |2 fast | |
| 650 | 7 | |a Stochastische Analysis |2 gnd |0 http://d-nb.info/gnd/4132272-1 | |
| 650 | 7 | |a Anomale Diffusion |2 gnd |0 http://d-nb.info/gnd/4532384-7 | |
| 650 | 7 | |a Gebrochene Analysis |2 gnd |0 http://d-nb.info/gnd/4722475-7 | |
| 650 | 7 | |a Gebrochene Analysis. |2 idszbz | |
| 650 | 7 | |a Stochastische Analysis. |2 idszbz | |
| 650 | 7 | |a Stochastisches Modell. |2 idszbz | |
| 650 | 7 | |a Diffusion. |2 idszbz | |
| 700 | 1 | |a Sikorskii, Alla., |e author. | |
| 776 | 0 | 8 | |i Print version: |a Meerschaert, Mark M., 1955- |t Stochastic models for fractional calculus. |d Berlin : De Gruyter, ©2011 |z 9783110258691 |
| 830 | 0 | |a De Gruyter studies in mathematics ; |v 43. |x 0179-0986 |0 http://id.loc.gov/authorities/names/n83742913 | |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2747065 |3 Volltext |
| 856 | 4 | 0 | |l FWS01 |p ZDB-4-EBA |q FWS_PDA_EBA |u https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430094 |3 Volltext |
| 938 | |a Askews and Holts Library Services |b ASKH |n AH25311050 | ||
| 938 | |a De Gruyter |b DEGR |n 9783110258165 | ||
| 938 | |a EBL - Ebook Library |b EBLB |n EBL835465 | ||
| 938 | |a ebrary |b EBRY |n ebr10527867 | ||
| 938 | |a EBSCOhost |b EBSC |n 430094 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n cis28650986 | ||
| 938 | |a YBP Library Services |b YANK |n 7310901 | ||
| 938 | |a Internet Archive |b INAR |n stochasticmodels0000meer | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn772845223 |
|---|---|
| _version_ | 1816881782615703552 |
| adam_text | |
| any_adam_object | |
| author | Meerschaert, Mark M., 1955- Sikorskii, Alla |
| author_GND | http://id.loc.gov/authorities/names/n92103385 |
| author_facet | Meerschaert, Mark M., 1955- Sikorskii, Alla |
| author_role | aut |
| author_sort | Meerschaert, Mark M., 1955- |
| author_variant | m m m mm mmm a s as |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA314 |
| callnumber-raw | QA314 .M484 2011 |
| callnumber-search | QA314 .M484 2011 |
| callnumber-sort | QA 3314 M484 42011 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SK 950 SK 820 |
| collection | ZDB-4-EBA |
| contents | Introduction ; The traditional diffusion model -- Fractional diffusion -- Fractional derivatives ; The Grünwald formula -- More fractional derivatives -- The Caputo derivative -- Time-fractional diffusion -- Stable limit distributions ; Infinitely divisible laws -- Stable characteristic functions -- Semigroups -- Poisson approximation -- Shifted Poisson approximation -- Triangular arrays -- One-sided stable limits -- Two-sided stable limits -- Continuous time random walks ; Regular variation -- Stable central limit theorem -- Continuous time random walks -- Convergence in Skorokhod space -- CTRW governing equations -- Computations in R ; R codes for fractional diffusion -- Sample path simulations Vector fractional diffusion ; Vector random walks -- Vector random walks with heavy tails -- Triangular arrays of random vectors -- Stable random vectors -- Vector fractional diffusion equation -- Operator stable laws -- Operator regular variation -- Generalized domains of attraction -- Applications and extensions ; LePage series representation -- Tempered stable laws -- Tempered fractional derivatives -- Pearson diffusions -- Fractional Pearson diffusions -- Fractional Brownian motion -- Fractional random fields -- Applications of fractional diffusion -- Applications of vector fractional diffusion. |
| ctrlnum | (OCoLC)772845223 |
| dewey-full | 515.83 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515.83 |
| dewey-search | 515.83 |
| dewey-sort | 3515.83 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>07157cam a2200889Mi 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn772845223</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr |n|---|||||</controlfield><controlfield tag="008">120116s2012 gw a ob 001 0 eng d</controlfield><datafield tag="010" ind1=" " ind2=" "><subfield code="z"> 2011036413</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">EBLCP</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">EBLCP</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">YDXCP</subfield><subfield code="d">N$T</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">DEBSZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">DEBBG</subfield><subfield code="d">E7B</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">COO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UIU</subfield><subfield code="d">AGLDB</subfield><subfield code="d">AZK</subfield><subfield code="d">YDX</subfield><subfield code="d">MOR</subfield><subfield code="d">PIFAG</subfield><subfield code="d">ZCU</subfield><subfield code="d">OTZ</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">MERUC</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DEGRU</subfield><subfield code="d">DKDLA</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VTS</subfield><subfield code="d">ICG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">STF</subfield><subfield code="d">LEAUB</subfield><subfield code="d">DKC</subfield><subfield code="d">AU@</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">UKAHL</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">TXI</subfield><subfield code="d">U3W</subfield><subfield code="d">WRM</subfield><subfield code="d">INT</subfield><subfield code="d">VT2</subfield><subfield code="d">WYU</subfield><subfield code="d">TKN</subfield><subfield code="d">HS0</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">VLY</subfield><subfield code="d">AUD</subfield><subfield code="d">AJS</subfield><subfield code="d">S2H</subfield><subfield code="d">OCLCO</subfield><subfield code="d">UKCRE</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">INARC</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield><subfield code="d">OCLCQ</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">785776485</subfield><subfield code="a">961527204</subfield><subfield code="a">979584734</subfield><subfield code="a">985273235</subfield><subfield code="a">985390879</subfield><subfield code="a">988416544</subfield><subfield code="a">988476448</subfield><subfield code="a">991924826</subfield><subfield code="a">994927097</subfield><subfield code="a">1013184144</subfield><subfield code="a">1018005982</subfield><subfield code="a">1037712939</subfield><subfield code="a">1038654813</subfield><subfield code="a">1038688029</subfield><subfield code="a">1055401727</subfield><subfield code="a">1058126024</subfield><subfield code="a">1059082058</subfield><subfield code="a">1064747765</subfield><subfield code="a">1081293925</subfield><subfield code="a">1096236715</subfield><subfield code="a">1119122738</subfield><subfield code="a">1152986076</subfield><subfield code="a">1162004094</subfield><subfield code="a">1264840415</subfield><subfield code="a">1290043454</subfield><subfield code="a">1300495312</subfield><subfield code="a">1388226056</subfield><subfield code="a">1392024835</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110258165</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110258161</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110258692</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110258691</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783110559149</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">3110559145</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1515/9783110258165</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)772845223</subfield><subfield code="z">(OCoLC)785776485</subfield><subfield code="z">(OCoLC)961527204</subfield><subfield code="z">(OCoLC)979584734</subfield><subfield code="z">(OCoLC)985273235</subfield><subfield code="z">(OCoLC)985390879</subfield><subfield code="z">(OCoLC)988416544</subfield><subfield code="z">(OCoLC)988476448</subfield><subfield code="z">(OCoLC)991924826</subfield><subfield code="z">(OCoLC)994927097</subfield><subfield code="z">(OCoLC)1013184144</subfield><subfield code="z">(OCoLC)1018005982</subfield><subfield code="z">(OCoLC)1037712939</subfield><subfield code="z">(OCoLC)1038654813</subfield><subfield code="z">(OCoLC)1038688029</subfield><subfield code="z">(OCoLC)1055401727</subfield><subfield code="z">(OCoLC)1058126024</subfield><subfield code="z">(OCoLC)1059082058</subfield><subfield code="z">(OCoLC)1064747765</subfield><subfield code="z">(OCoLC)1081293925</subfield><subfield code="z">(OCoLC)1096236715</subfield><subfield code="z">(OCoLC)1119122738</subfield><subfield code="z">(OCoLC)1152986076</subfield><subfield code="z">(OCoLC)1162004094</subfield><subfield code="z">(OCoLC)1264840415</subfield><subfield code="z">(OCoLC)1290043454</subfield><subfield code="z">(OCoLC)1300495312</subfield><subfield code="z">(OCoLC)1388226056</subfield><subfield code="z">(OCoLC)1392024835</subfield></datafield><datafield tag="037" ind1=" " ind2=" "><subfield code="a">835465</subfield><subfield code="b">Proquest Ebook Central</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA314 .M484 2011</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">005000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">034000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">515.83</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 950</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="2">rvk</subfield><subfield code="0">(DE-625)rvk/143258:</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Meerschaert, Mark M.,</subfield><subfield code="d">1955-</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJvtdRBcfXWGf46Jc7dfbd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n92103385</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Stochastic models for fractional calculus /</subfield><subfield code="c">Mark M. Meerschaert, Alla Sikorskii.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Berlin :</subfield><subfield code="b">De Gruyter,</subfield><subfield code="c">©2012.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (x, 294 pages) :</subfield><subfield code="b">illustrations</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">computer</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">online resource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="347" ind1=" " ind2=" "><subfield code="a">data file</subfield><subfield code="2">rda</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">De Gruyter studies in mathematics,</subfield><subfield code="x">0179-0986 ;</subfield><subfield code="v">43</subfield></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 279-288), and index.</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Introduction ;</subfield><subfield code="t">The traditional diffusion model --</subfield><subfield code="t">Fractional diffusion --</subfield><subfield code="t">Fractional derivatives ;</subfield><subfield code="t">The Grünwald formula --</subfield><subfield code="t">More fractional derivatives --</subfield><subfield code="t">The Caputo derivative --</subfield><subfield code="t">Time-fractional diffusion --</subfield><subfield code="t">Stable limit distributions ;</subfield><subfield code="t">Infinitely divisible laws --</subfield><subfield code="t">Stable characteristic functions --</subfield><subfield code="t">Semigroups --</subfield><subfield code="t">Poisson approximation --</subfield><subfield code="t">Shifted Poisson approximation --</subfield><subfield code="t">Triangular arrays --</subfield><subfield code="t">One-sided stable limits --</subfield><subfield code="t">Two-sided stable limits --</subfield><subfield code="t">Continuous time random walks ;</subfield><subfield code="t">Regular variation --</subfield><subfield code="t">Stable central limit theorem --</subfield><subfield code="t">Continuous time random walks --</subfield><subfield code="t">Convergence in Skorokhod space --</subfield><subfield code="t">CTRW governing equations --</subfield><subfield code="t">Computations in R ;</subfield><subfield code="t">R codes for fractional diffusion --</subfield><subfield code="t">Sample path simulations</subfield></datafield><datafield tag="505" ind1="0" ind2="0"><subfield code="t">Vector fractional diffusion ;</subfield><subfield code="t">Vector random walks --</subfield><subfield code="t">Vector random walks with heavy tails --</subfield><subfield code="t">Triangular arrays of random vectors --</subfield><subfield code="t">Stable random vectors --</subfield><subfield code="t">Vector fractional diffusion equation --</subfield><subfield code="t">Operator stable laws --</subfield><subfield code="t">Operator regular variation --</subfield><subfield code="t">Generalized domains of attraction --</subfield><subfield code="t">Applications and extensions ;</subfield><subfield code="t">LePage series representation --</subfield><subfield code="t">Tempered stable laws --</subfield><subfield code="t">Tempered fractional derivatives --</subfield><subfield code="t">Pearson diffusions --</subfield><subfield code="t">Fractional Pearson diffusions --</subfield><subfield code="t">Fractional Brownian motion --</subfield><subfield code="t">Fractional random fields --</subfield><subfield code="t">Applications of fractional diffusion --</subfield><subfield code="t">Applications of vector fractional diffusion.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">In English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Fractional calculus.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh93004015</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Diffusion processes.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85037941</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Stochastic analysis.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85128175</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Dérivées fractionnaires.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Processus de diffusion.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Analyse stochastique.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Calculus.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Mathematical Analysis.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Diffusion processes</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Fractional calculus</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastic analysis</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastische Analysis</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4132272-1</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Anomale Diffusion</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4532384-7</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Gebrochene Analysis</subfield><subfield code="2">gnd</subfield><subfield code="0">http://d-nb.info/gnd/4722475-7</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Gebrochene Analysis.</subfield><subfield code="2">idszbz</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastische Analysis.</subfield><subfield code="2">idszbz</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Stochastisches Modell.</subfield><subfield code="2">idszbz</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Diffusion.</subfield><subfield code="2">idszbz</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Sikorskii, Alla.,</subfield><subfield code="e">author.</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Meerschaert, Mark M., 1955-</subfield><subfield code="t">Stochastic models for fractional calculus.</subfield><subfield code="d">Berlin : De Gruyter, ©2011</subfield><subfield code="z">9783110258691</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">De Gruyter studies in mathematics ;</subfield><subfield code="v">43.</subfield><subfield code="x">0179-0986</subfield><subfield code="0">http://id.loc.gov/authorities/names/n83742913</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2747065</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="l">FWS01</subfield><subfield code="p">ZDB-4-EBA</subfield><subfield code="q">FWS_PDA_EBA</subfield><subfield code="u">https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430094</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH25311050</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">De Gruyter</subfield><subfield code="b">DEGR</subfield><subfield code="n">9783110258165</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBL - Ebook Library</subfield><subfield code="b">EBLB</subfield><subfield code="n">EBL835465</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10527867</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">430094</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">cis28650986</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">7310901</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Internet Archive</subfield><subfield code="b">INAR</subfield><subfield code="n">stochasticmodels0000meer</subfield></datafield><datafield tag="994" ind1=" " ind2=" "><subfield code="a">92</subfield><subfield code="b">GEBAY</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-4-EBA</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-863</subfield></datafield></record></collection> |
| id | ZDB-4-EBA-ocn772845223 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:11Z |
| institution | BVB |
| isbn | 9783110258165 3110258161 3110258692 9783110258691 9783110559149 3110559145 |
| issn | 0179-0986 ; |
| language | English |
| oclc_num | 772845223 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (x, 294 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | De Gruyter, |
| record_format | marc |
| series | De Gruyter studies in mathematics ; |
| series2 | De Gruyter studies in mathematics, |
| spelling | Meerschaert, Mark M., 1955- https://id.oclc.org/worldcat/entity/E39PBJvtdRBcfXWGf46Jc7dfbd http://id.loc.gov/authorities/names/n92103385 Stochastic models for fractional calculus / Mark M. Meerschaert, Alla Sikorskii. Berlin : De Gruyter, ©2012. 1 online resource (x, 294 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier data file rda De Gruyter studies in mathematics, 0179-0986 ; 43 Includes bibliographical references (pages 279-288), and index. Introduction ; The traditional diffusion model -- Fractional diffusion -- Fractional derivatives ; The Grünwald formula -- More fractional derivatives -- The Caputo derivative -- Time-fractional diffusion -- Stable limit distributions ; Infinitely divisible laws -- Stable characteristic functions -- Semigroups -- Poisson approximation -- Shifted Poisson approximation -- Triangular arrays -- One-sided stable limits -- Two-sided stable limits -- Continuous time random walks ; Regular variation -- Stable central limit theorem -- Continuous time random walks -- Convergence in Skorokhod space -- CTRW governing equations -- Computations in R ; R codes for fractional diffusion -- Sample path simulations Vector fractional diffusion ; Vector random walks -- Vector random walks with heavy tails -- Triangular arrays of random vectors -- Stable random vectors -- Vector fractional diffusion equation -- Operator stable laws -- Operator regular variation -- Generalized domains of attraction -- Applications and extensions ; LePage series representation -- Tempered stable laws -- Tempered fractional derivatives -- Pearson diffusions -- Fractional Pearson diffusions -- Fractional Brownian motion -- Fractional random fields -- Applications of fractional diffusion -- Applications of vector fractional diffusion. This monograph develops the basic theory of fractional calculus and anomalous diffusion, from the point of view of probability. In this book, we will see how fractional calculus and anomalous diffusion can be understood at a deep and intuitive level, using ideas from probability. It covers basic limit theorems for random variables and random vectors with heavy tails. This includes regular variation, triangular arrays, infinitely divisible laws, random walks, and stochastic process convergence in the Skorokhod topology. The basic ideas of fractional calculus and anomalous diffusion are closely connected with heavy tail limit theorems. Heavy tails are applied in finance, insurance, physics, geophysics, cell biology, ecology, medicine, and computer engineering. The goal of this book is to prepare graduate students in probability for research in the area of fractional calculus, anomalous diffusion, and heavy tails. Print version record. In English. Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Diffusion processes. http://id.loc.gov/authorities/subjects/sh85037941 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Dérivées fractionnaires. Processus de diffusion. Analyse stochastique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Stochastische Analysis gnd http://d-nb.info/gnd/4132272-1 Anomale Diffusion gnd http://d-nb.info/gnd/4532384-7 Gebrochene Analysis gnd http://d-nb.info/gnd/4722475-7 Gebrochene Analysis. idszbz Stochastische Analysis. idszbz Stochastisches Modell. idszbz Diffusion. idszbz Sikorskii, Alla., author. Print version: Meerschaert, Mark M., 1955- Stochastic models for fractional calculus. Berlin : De Gruyter, ©2011 9783110258691 De Gruyter studies in mathematics ; 43. 0179-0986 http://id.loc.gov/authorities/names/n83742913 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2747065 Volltext FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430094 Volltext |
| spellingShingle | Meerschaert, Mark M., 1955- Sikorskii, Alla Stochastic models for fractional calculus / De Gruyter studies in mathematics ; Introduction ; The traditional diffusion model -- Fractional diffusion -- Fractional derivatives ; The Grünwald formula -- More fractional derivatives -- The Caputo derivative -- Time-fractional diffusion -- Stable limit distributions ; Infinitely divisible laws -- Stable characteristic functions -- Semigroups -- Poisson approximation -- Shifted Poisson approximation -- Triangular arrays -- One-sided stable limits -- Two-sided stable limits -- Continuous time random walks ; Regular variation -- Stable central limit theorem -- Continuous time random walks -- Convergence in Skorokhod space -- CTRW governing equations -- Computations in R ; R codes for fractional diffusion -- Sample path simulations Vector fractional diffusion ; Vector random walks -- Vector random walks with heavy tails -- Triangular arrays of random vectors -- Stable random vectors -- Vector fractional diffusion equation -- Operator stable laws -- Operator regular variation -- Generalized domains of attraction -- Applications and extensions ; LePage series representation -- Tempered stable laws -- Tempered fractional derivatives -- Pearson diffusions -- Fractional Pearson diffusions -- Fractional Brownian motion -- Fractional random fields -- Applications of fractional diffusion -- Applications of vector fractional diffusion. Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Diffusion processes. http://id.loc.gov/authorities/subjects/sh85037941 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Dérivées fractionnaires. Processus de diffusion. Analyse stochastique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Stochastische Analysis gnd http://d-nb.info/gnd/4132272-1 Anomale Diffusion gnd http://d-nb.info/gnd/4532384-7 Gebrochene Analysis gnd http://d-nb.info/gnd/4722475-7 Gebrochene Analysis. idszbz Stochastische Analysis. idszbz Stochastisches Modell. idszbz Diffusion. idszbz |
| subject_GND | http://id.loc.gov/authorities/subjects/sh93004015 http://id.loc.gov/authorities/subjects/sh85037941 http://id.loc.gov/authorities/subjects/sh85128175 http://d-nb.info/gnd/4132272-1 http://d-nb.info/gnd/4532384-7 http://d-nb.info/gnd/4722475-7 |
| title | Stochastic models for fractional calculus / |
| title_alt | Introduction ; The traditional diffusion model -- Fractional diffusion -- Fractional derivatives ; The Grünwald formula -- More fractional derivatives -- The Caputo derivative -- Time-fractional diffusion -- Stable limit distributions ; Infinitely divisible laws -- Stable characteristic functions -- Semigroups -- Poisson approximation -- Shifted Poisson approximation -- Triangular arrays -- One-sided stable limits -- Two-sided stable limits -- Continuous time random walks ; Regular variation -- Stable central limit theorem -- Continuous time random walks -- Convergence in Skorokhod space -- CTRW governing equations -- Computations in R ; R codes for fractional diffusion -- Sample path simulations Vector fractional diffusion ; Vector random walks -- Vector random walks with heavy tails -- Triangular arrays of random vectors -- Stable random vectors -- Vector fractional diffusion equation -- Operator stable laws -- Operator regular variation -- Generalized domains of attraction -- Applications and extensions ; LePage series representation -- Tempered stable laws -- Tempered fractional derivatives -- Pearson diffusions -- Fractional Pearson diffusions -- Fractional Brownian motion -- Fractional random fields -- Applications of fractional diffusion -- Applications of vector fractional diffusion. |
| title_auth | Stochastic models for fractional calculus / |
| title_exact_search | Stochastic models for fractional calculus / |
| title_full | Stochastic models for fractional calculus / Mark M. Meerschaert, Alla Sikorskii. |
| title_fullStr | Stochastic models for fractional calculus / Mark M. Meerschaert, Alla Sikorskii. |
| title_full_unstemmed | Stochastic models for fractional calculus / Mark M. Meerschaert, Alla Sikorskii. |
| title_short | Stochastic models for fractional calculus / |
| title_sort | stochastic models for fractional calculus |
| topic | Fractional calculus. http://id.loc.gov/authorities/subjects/sh93004015 Diffusion processes. http://id.loc.gov/authorities/subjects/sh85037941 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Dérivées fractionnaires. Processus de diffusion. Analyse stochastique. MATHEMATICS Calculus. bisacsh MATHEMATICS Mathematical Analysis. bisacsh Diffusion processes fast Fractional calculus fast Stochastic analysis fast Stochastische Analysis gnd http://d-nb.info/gnd/4132272-1 Anomale Diffusion gnd http://d-nb.info/gnd/4532384-7 Gebrochene Analysis gnd http://d-nb.info/gnd/4722475-7 Gebrochene Analysis. idszbz Stochastische Analysis. idszbz Stochastisches Modell. idszbz Diffusion. idszbz |
| topic_facet | Fractional calculus. Diffusion processes. Stochastic analysis. Dérivées fractionnaires. Processus de diffusion. Analyse stochastique. MATHEMATICS Calculus. MATHEMATICS Mathematical Analysis. Diffusion processes Fractional calculus Stochastic analysis Stochastische Analysis Anomale Diffusion Gebrochene Analysis Gebrochene Analysis. Stochastische Analysis. Stochastisches Modell. Diffusion. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=2747065 https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=430094 |
| work_keys_str_mv | AT meerschaertmarkm stochasticmodelsforfractionalcalculus AT sikorskiialla stochasticmodelsforfractionalcalculus |