Generalized functionals of Brownian motion and their applications: nonlinear functionals of fundamental stochastic processes
This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as sp...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Pub. Co.
c2012
|
| Schlagworte: | |
| Online-Zugang: | FHN01 Volltext |
| Zusammenfassung: | This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject |
| Beschreibung: | xiv, 299 p |
| ISBN: | 9789814366373 |
Internformat
MARC
| LEADER | 00000nmm a2200000zc 4500 | ||
|---|---|---|---|
| 001 | BV044638702 | ||
| 003 | DE-604 | ||
| 005 | 00000000000000.0 | ||
| 007 | cr|uuu---uuuuu | ||
| 008 | 171120s2012 |||| o||u| ||||||eng d | ||
| 020 | |a 9789814366373 |c electronic bk. |9 978-981-4366-37-3 | ||
| 024 | 7 | |a 10.1142/8251 |2 doi | |
| 035 | |a (ZDB-124-WOP)00002539 | ||
| 035 | |a (OCoLC)1012646469 | ||
| 035 | |a (DE-599)BVBBV044638702 | ||
| 040 | |a DE-604 |b ger |e aacr | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-92 | ||
| 082 | 0 | |a 519.23 |2 22 | |
| 084 | |a SK 820 |0 (DE-625)143258: |2 rvk | ||
| 100 | 1 | |a Ahmed, N. U. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Generalized functionals of Brownian motion and their applications |b nonlinear functionals of fundamental stochastic processes |c N. U. Ahmed |
| 264 | 1 | |a Singapore |b World Scientific Pub. Co. |c c2012 | |
| 300 | |a xiv, 299 p | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b c |2 rdamedia | ||
| 338 | |b cr |2 rdacarrier | ||
| 520 | |a This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject | ||
| 650 | 4 | |a Stochastic processes | |
| 650 | 4 | |a Brownian motion processes | |
| 650 | 0 | 7 | |a Nichtlineares Funktional |0 (DE-588)4604704-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Brownsche Bewegung |0 (DE-588)4128328-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Brownsche Bewegung |0 (DE-588)4128328-4 |D s |
| 689 | 0 | 1 | |a Stochastischer Prozess |0 (DE-588)4057630-9 |D s |
| 689 | 0 | 2 | |a Nichtlineares Funktional |0 (DE-588)4604704-9 |D s |
| 689 | 0 | |8 1\p |5 DE-604 | |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9789814366366 |
| 776 | 0 | 8 | |i Erscheint auch als |n Druck-Ausgabe |z 9814366366 |
| 856 | 4 | 0 | |u http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc |x Verlag |z URL des Erstveroeffentlichers |3 Volltext |
| 912 | |a ZDB-124-WOP | ||
| 999 | |a oai:aleph.bib-bvb.de:BVB01-030036675 | ||
| 883 | 1 | |8 1\p |a cgwrk |d 20201028 |q DE-101 |u https://d-nb.info/provenance/plan#cgwrk | |
| 966 | e | |u http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc |l FHN01 |p ZDB-124-WOP |q FHN_PDA_WOP |x Verlag |3 Volltext | |
Datensatz im Suchindex
| _version_ | 1804178055870021632 |
|---|---|
| any_adam_object | |
| author | Ahmed, N. U. |
| author_facet | Ahmed, N. U. |
| author_role | aut |
| author_sort | Ahmed, N. U. |
| author_variant | n u a nu nua |
| building | Verbundindex |
| bvnumber | BV044638702 |
| classification_rvk | SK 820 |
| collection | ZDB-124-WOP |
| ctrlnum | (ZDB-124-WOP)00002539 (OCoLC)1012646469 (DE-599)BVBBV044638702 |
| dewey-full | 519.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.23 |
| dewey-search | 519.23 |
| dewey-sort | 3519.23 |
| 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>03427nmm a2200493zc 4500</leader><controlfield tag="001">BV044638702</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">00000000000000.0</controlfield><controlfield tag="007">cr|uuu---uuuuu</controlfield><controlfield tag="008">171120s2012 |||| o||u| ||||||eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789814366373</subfield><subfield code="c">electronic bk.</subfield><subfield code="9">978-981-4366-37-3</subfield></datafield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1142/8251</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(ZDB-124-WOP)00002539 </subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)1012646469</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV044638702</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">aacr</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-92</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">519.23</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SK 820</subfield><subfield code="0">(DE-625)143258:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ahmed, N. U.</subfield><subfield code="e">Verfasser</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Generalized functionals of Brownian motion and their applications</subfield><subfield code="b">nonlinear functionals of fundamental stochastic processes</subfield><subfield code="c">N. U. Ahmed</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Singapore</subfield><subfield code="b">World Scientific Pub. Co.</subfield><subfield code="c">c2012</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">xiv, 299 p</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Stochastic processes</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Brownian motion processes</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Nichtlineares Funktional</subfield><subfield code="0">(DE-588)4604704-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Brownsche Bewegung</subfield><subfield code="0">(DE-588)4128328-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Brownsche Bewegung</subfield><subfield code="0">(DE-588)4128328-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Stochastischer Prozess</subfield><subfield code="0">(DE-588)4057630-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Nichtlineares Funktional</subfield><subfield code="0">(DE-588)4604704-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="8">1\p</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9789814366366</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Erscheint auch als</subfield><subfield code="n">Druck-Ausgabe</subfield><subfield code="z">9814366366</subfield></datafield><datafield tag="856" ind1="4" ind2="0"><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc</subfield><subfield code="x">Verlag</subfield><subfield code="z">URL des Erstveroeffentlichers</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="912" ind1=" " ind2=" "><subfield code="a">ZDB-124-WOP</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-030036675</subfield></datafield><datafield tag="883" ind1="1" ind2=" "><subfield code="8">1\p</subfield><subfield code="a">cgwrk</subfield><subfield code="d">20201028</subfield><subfield code="q">DE-101</subfield><subfield code="u">https://d-nb.info/provenance/plan#cgwrk</subfield></datafield><datafield tag="966" ind1="e" ind2=" "><subfield code="u">http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc</subfield><subfield code="l">FHN01</subfield><subfield code="p">ZDB-124-WOP</subfield><subfield code="q">FHN_PDA_WOP</subfield><subfield code="x">Verlag</subfield><subfield code="3">Volltext</subfield></datafield></record></collection> |
| id | DE-604.BV044638702 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:57:54Z |
| institution | BVB |
| isbn | 9789814366373 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-030036675 |
| oclc_num | 1012646469 |
| open_access_boolean | |
| owner | DE-92 |
| owner_facet | DE-92 |
| physical | xiv, 299 p |
| psigel | ZDB-124-WOP ZDB-124-WOP FHN_PDA_WOP |
| publishDate | 2012 |
| publishDateSearch | 2012 |
| publishDateSort | 2012 |
| publisher | World Scientific Pub. Co. |
| record_format | marc |
| spelling | Ahmed, N. U. Verfasser aut Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes N. U. Ahmed Singapore World Scientific Pub. Co. c2012 xiv, 299 p txt rdacontent c rdamedia cr rdacarrier This invaluable research monograph presents a unified and fascinating theory of generalized functionals of Brownian motion and other fundamental processes such as fractional Brownian motion and Levy process - covering the classical Wiener-Ito class including the generalized functionals of Hida as special cases, among others. It presents a thorough and comprehensive treatment of the Wiener-Sobolev spaces and their duals, as well as Malliavin calculus with their applications. The presentation is lucid and logical, and is based on a solid foundation of analysis and topology. The monograph develops the notions of compactness and weak compactness on these abstract Fock spaces and their duals, clearly demonstrating their nontrivial applications to stochastic differential equations in finite and infinite dimensional Hilbert spaces, optimization and optimal control problems. Readers will find the book an interesting and easy read as materials are presented in a systematic manner with a complete analysis of classical and generalized functionals of scalar Brownian motion, Gaussian random fields and their vector versions in the increasing order of generality. It starts with abstract Fourier analysis on the Wiener measure space where a striking similarity of the celebrated Riesz-Fischer theorem for separable Hilbert spaces and the space of Wiener-Ito functionals is drawn out, thus providing a clear insight into the subject Stochastic processes Brownian motion processes Nichtlineares Funktional (DE-588)4604704-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 gnd rswk-swf Stochastischer Prozess (DE-588)4057630-9 gnd rswk-swf Brownsche Bewegung (DE-588)4128328-4 s Stochastischer Prozess (DE-588)4057630-9 s Nichtlineares Funktional (DE-588)4604704-9 s 1\p DE-604 Erscheint auch als Druck-Ausgabe 9789814366366 Erscheint auch als Druck-Ausgabe 9814366366 http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc Verlag URL des Erstveroeffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Ahmed, N. U. Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes Stochastic processes Brownian motion processes Nichtlineares Funktional (DE-588)4604704-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| subject_GND | (DE-588)4604704-9 (DE-588)4128328-4 (DE-588)4057630-9 |
| title | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes |
| title_auth | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes |
| title_exact_search | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes |
| title_full | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes N. U. Ahmed |
| title_fullStr | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes N. U. Ahmed |
| title_full_unstemmed | Generalized functionals of Brownian motion and their applications nonlinear functionals of fundamental stochastic processes N. U. Ahmed |
| title_short | Generalized functionals of Brownian motion and their applications |
| title_sort | generalized functionals of brownian motion and their applications nonlinear functionals of fundamental stochastic processes |
| title_sub | nonlinear functionals of fundamental stochastic processes |
| topic | Stochastic processes Brownian motion processes Nichtlineares Funktional (DE-588)4604704-9 gnd Brownsche Bewegung (DE-588)4128328-4 gnd Stochastischer Prozess (DE-588)4057630-9 gnd |
| topic_facet | Stochastic processes Brownian motion processes Nichtlineares Funktional Brownsche Bewegung Stochastischer Prozess |
| url | http://www.worldscientific.com/worldscibooks/10.1142/8251#t=toc |
| work_keys_str_mv | AT ahmednu generalizedfunctionalsofbrownianmotionandtheirapplicationsnonlinearfunctionalsoffundamentalstochasticprocesses |