Random fields estimation /:
This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Hackensack, NJ :
World Scientific,
©2005.
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory. |
| Beschreibung: | 1 online resource (xiii, 373 pages) |
| Bibliographie: | Includes bibliographical references (pages 363-369) and index. |
| ISBN: | 9812565361 9789812565365 9812703152 9789812703156 1281899143 9781281899149 9786611899141 6611899146 |
Internformat
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | ZDB-4-EBA-ocn182530762 | ||
| 003 | OCoLC | ||
| 005 | 20241004212047.0 | ||
| 006 | m o d | ||
| 007 | cr cn||||||||| | ||
| 008 | 060927s2005 nju ob 001 0 eng d | ||
| 040 | |a COCUF |b eng |e pn |c COCUF |d OCLCG |d OCLCQ |d N$T |d YDXCP |d IDEBK |d OCLCQ |d DKDLA |d ADU |d E7B |d OCLCQ |d OCLCF |d OCLCO |d OCLCQ |d AZK |d COCUF |d AGLDB |d MOR |d PIFBR |d OCLCQ |d WRM |d VTS |d INT |d VT2 |d OCLCQ |d WYU |d OCLCQ |d LEAUB |d JBG |d UKAHL |d VLY |d OCLCQ |d OCLCO |d M8D |d SFB |d OCLCO |d OCLCQ |d OCLCO |d OCLCL | ||
| 019 | |a 77731597 |a 148811683 |a 473096591 |a 482675692 |a 614965400 |a 648231060 |a 722567440 |a 748531008 |a 815746178 |a 888731368 |a 961552888 |a 962682396 |a 1162533048 |a 1241883414 |a 1290073331 |a 1300509239 | ||
| 020 | |a 9812565361 | ||
| 020 | |a 9789812565365 | ||
| 020 | |a 9812703152 |q (electronic bk.) | ||
| 020 | |a 9789812703156 |q (electronic bk.) | ||
| 020 | |a 1281899143 | ||
| 020 | |a 9781281899149 | ||
| 020 | |a 9786611899141 | ||
| 020 | |a 6611899146 | ||
| 035 | |a (OCoLC)182530762 |z (OCoLC)77731597 |z (OCoLC)148811683 |z (OCoLC)473096591 |z (OCoLC)482675692 |z (OCoLC)614965400 |z (OCoLC)648231060 |z (OCoLC)722567440 |z (OCoLC)748531008 |z (OCoLC)815746178 |z (OCoLC)888731368 |z (OCoLC)961552888 |z (OCoLC)962682396 |z (OCoLC)1162533048 |z (OCoLC)1241883414 |z (OCoLC)1290073331 |z (OCoLC)1300509239 | ||
| 050 | 4 | |a QA274.45 |b .R348 2005eb | |
| 072 | 7 | |a MAT |x 029000 |2 bisacsh | |
| 072 | 7 | |a PBT |2 bicssc | |
| 082 | 7 | |a 519.2 |2 22 | |
| 049 | |a MAIN | ||
| 100 | 1 | |a Ramm, A. G. |q (Alexander G.) |1 https://id.oclc.org/worldcat/entity/E39PBJht6c7MRHvFtQDQJ4MVmd |0 http://id.loc.gov/authorities/names/n80129782 | |
| 245 | 1 | 0 | |a Random fields estimation / |c Alexander G. Ramm. |
| 260 | |a Hackensack, NJ : |b World Scientific, |c ©2005. | ||
| 300 | |a 1 online resource (xiii, 373 pages) | ||
| 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 | ||
| 504 | |a Includes bibliographical references (pages 363-369) and index. | ||
| 505 | 0 | |a Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space. | |
| 520 | |a This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory. | ||
| 588 | 0 | |a Print version record. | |
| 546 | |a English. | ||
| 650 | 0 | |a Random fields. |0 http://id.loc.gov/authorities/subjects/sh85111347 | |
| 650 | 0 | |a Estimation theory. |0 http://id.loc.gov/authorities/subjects/sh85044957 | |
| 650 | 6 | |a Champs aléatoires. | |
| 650 | 6 | |a Théorie de l'estimation. | |
| 650 | 7 | |a MATHEMATICS |x Probability & Statistics |x General. |2 bisacsh | |
| 650 | 7 | |a Estimation theory |2 fast | |
| 650 | 7 | |a Random fields |2 fast | |
| 700 | 1 | |a Ramm, A. G. |q (Alexander G.). |t Random fields estimation theory. | |
| 758 | |i has work: |a Random fields estimation (Text) |1 https://id.oclc.org/worldcat/entity/E39PCFrvXGMPFc44mGRdpGdjVK |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Ramm, A.G. (Alexander G.). |t Random fields estimation. |d Hackensack, NJ : World Scientific, ©2005 |w (DLC) 2006299148 |
| 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=174689 |3 Volltext |
| 936 | |a BATCHLOAD | ||
| 938 | |a Askews and Holts Library Services |b ASKH |n AH24683960 | ||
| 938 | |a ebrary |b EBRY |n ebr10173937 | ||
| 938 | |a EBSCOhost |b EBSC |n 174689 | ||
| 938 | |a ProQuest MyiLibrary Digital eBook Collection |b IDEB |n 189914 | ||
| 938 | |a YBP Library Services |b YANK |n 2507574 | ||
| 994 | |a 92 |b GEBAY | ||
| 912 | |a ZDB-4-EBA | ||
| 049 | |a DE-863 | ||
Datensatz im Suchindex
| DE-BY-FWS_katkey | ZDB-4-EBA-ocn182530762 |
|---|---|
| _version_ | 1816881657845645313 |
| adam_text | |
| any_adam_object | |
| author | Ramm, A. G. (Alexander G.) |
| author2 | Ramm, A. G. (Alexander G.) |
| author2_role | |
| author2_variant | a g r ag agr |
| author_GND | http://id.loc.gov/authorities/names/n80129782 |
| author_facet | Ramm, A. G. (Alexander G.) Ramm, A. G. (Alexander G.) |
| author_role | |
| author_sort | Ramm, A. G. |
| author_variant | a g r ag agr |
| building | Verbundindex |
| bvnumber | localFWS |
| callnumber-first | Q - Science |
| callnumber-label | QA274 |
| callnumber-raw | QA274.45 .R348 2005eb |
| callnumber-search | QA274.45 .R348 2005eb |
| callnumber-sort | QA 3274.45 R348 42005EB |
| callnumber-subject | QA - Mathematics |
| collection | ZDB-4-EBA |
| contents | Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space. |
| ctrlnum | (OCoLC)182530762 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| 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>07228cam a2200661 a 4500</leader><controlfield tag="001">ZDB-4-EBA-ocn182530762</controlfield><controlfield tag="003">OCoLC</controlfield><controlfield tag="005">20241004212047.0</controlfield><controlfield tag="006">m o d </controlfield><controlfield tag="007">cr cn|||||||||</controlfield><controlfield tag="008">060927s2005 nju ob 001 0 eng d</controlfield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">COCUF</subfield><subfield code="b">eng</subfield><subfield code="e">pn</subfield><subfield code="c">COCUF</subfield><subfield code="d">OCLCG</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">N$T</subfield><subfield code="d">YDXCP</subfield><subfield code="d">IDEBK</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">DKDLA</subfield><subfield code="d">ADU</subfield><subfield code="d">E7B</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCF</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">AZK</subfield><subfield code="d">COCUF</subfield><subfield code="d">AGLDB</subfield><subfield code="d">MOR</subfield><subfield code="d">PIFBR</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WRM</subfield><subfield code="d">VTS</subfield><subfield code="d">INT</subfield><subfield code="d">VT2</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">WYU</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">LEAUB</subfield><subfield code="d">JBG</subfield><subfield code="d">UKAHL</subfield><subfield code="d">VLY</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">M8D</subfield><subfield code="d">SFB</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCQ</subfield><subfield code="d">OCLCO</subfield><subfield code="d">OCLCL</subfield></datafield><datafield tag="019" ind1=" " ind2=" "><subfield code="a">77731597</subfield><subfield code="a">148811683</subfield><subfield code="a">473096591</subfield><subfield code="a">482675692</subfield><subfield code="a">614965400</subfield><subfield code="a">648231060</subfield><subfield code="a">722567440</subfield><subfield code="a">748531008</subfield><subfield code="a">815746178</subfield><subfield code="a">888731368</subfield><subfield code="a">961552888</subfield><subfield code="a">962682396</subfield><subfield code="a">1162533048</subfield><subfield code="a">1241883414</subfield><subfield code="a">1290073331</subfield><subfield code="a">1300509239</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812565361</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812565365</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9812703152</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9789812703156</subfield><subfield code="q">(electronic bk.)</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1281899143</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781281899149</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9786611899141</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">6611899146</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)182530762</subfield><subfield code="z">(OCoLC)77731597</subfield><subfield code="z">(OCoLC)148811683</subfield><subfield code="z">(OCoLC)473096591</subfield><subfield code="z">(OCoLC)482675692</subfield><subfield code="z">(OCoLC)614965400</subfield><subfield code="z">(OCoLC)648231060</subfield><subfield code="z">(OCoLC)722567440</subfield><subfield code="z">(OCoLC)748531008</subfield><subfield code="z">(OCoLC)815746178</subfield><subfield code="z">(OCoLC)888731368</subfield><subfield code="z">(OCoLC)961552888</subfield><subfield code="z">(OCoLC)962682396</subfield><subfield code="z">(OCoLC)1162533048</subfield><subfield code="z">(OCoLC)1241883414</subfield><subfield code="z">(OCoLC)1290073331</subfield><subfield code="z">(OCoLC)1300509239</subfield></datafield><datafield tag="050" ind1=" " ind2="4"><subfield code="a">QA274.45</subfield><subfield code="b">.R348 2005eb</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">MAT</subfield><subfield code="x">029000</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="072" ind1=" " ind2="7"><subfield code="a">PBT</subfield><subfield code="2">bicssc</subfield></datafield><datafield tag="082" ind1="7" ind2=" "><subfield code="a">519.2</subfield><subfield code="2">22</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">MAIN</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Ramm, A. G.</subfield><subfield code="q">(Alexander G.)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PBJht6c7MRHvFtQDQJ4MVmd</subfield><subfield code="0">http://id.loc.gov/authorities/names/n80129782</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Random fields estimation /</subfield><subfield code="c">Alexander G. Ramm.</subfield></datafield><datafield tag="260" ind1=" " ind2=" "><subfield code="a">Hackensack, NJ :</subfield><subfield code="b">World Scientific,</subfield><subfield code="c">©2005.</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">1 online resource (xiii, 373 pages)</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></datafield><datafield tag="504" ind1=" " ind2=" "><subfield code="a">Includes bibliographical references (pages 363-369) and index.</subfield></datafield><datafield tag="505" ind1="0" ind2=" "><subfield code="a">Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory.</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="546" ind1=" " ind2=" "><subfield code="a">English.</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Random fields.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85111347</subfield></datafield><datafield tag="650" ind1=" " ind2="0"><subfield code="a">Estimation theory.</subfield><subfield code="0">http://id.loc.gov/authorities/subjects/sh85044957</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Champs aléatoires.</subfield></datafield><datafield tag="650" ind1=" " ind2="6"><subfield code="a">Théorie de l'estimation.</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">MATHEMATICS</subfield><subfield code="x">Probability & Statistics</subfield><subfield code="x">General.</subfield><subfield code="2">bisacsh</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Estimation theory</subfield><subfield code="2">fast</subfield></datafield><datafield tag="650" ind1=" " ind2="7"><subfield code="a">Random fields</subfield><subfield code="2">fast</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ramm, A. G.</subfield><subfield code="q">(Alexander G.).</subfield><subfield code="t">Random fields estimation theory.</subfield></datafield><datafield tag="758" ind1=" " ind2=" "><subfield code="i">has work:</subfield><subfield code="a">Random fields estimation (Text)</subfield><subfield code="1">https://id.oclc.org/worldcat/entity/E39PCFrvXGMPFc44mGRdpGdjVK</subfield><subfield code="4">https://id.oclc.org/worldcat/ontology/hasWork</subfield></datafield><datafield tag="776" ind1="0" ind2="8"><subfield code="i">Print version:</subfield><subfield code="a">Ramm, A.G. (Alexander G.).</subfield><subfield code="t">Random fields estimation.</subfield><subfield code="d">Hackensack, NJ : World Scientific, ©2005</subfield><subfield code="w">(DLC) 2006299148</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=174689</subfield><subfield code="3">Volltext</subfield></datafield><datafield tag="936" ind1=" " ind2=" "><subfield code="a">BATCHLOAD</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">Askews and Holts Library Services</subfield><subfield code="b">ASKH</subfield><subfield code="n">AH24683960</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ebrary</subfield><subfield code="b">EBRY</subfield><subfield code="n">ebr10173937</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">EBSCOhost</subfield><subfield code="b">EBSC</subfield><subfield code="n">174689</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">ProQuest MyiLibrary Digital eBook Collection</subfield><subfield code="b">IDEB</subfield><subfield code="n">189914</subfield></datafield><datafield tag="938" ind1=" " ind2=" "><subfield code="a">YBP Library Services</subfield><subfield code="b">YANK</subfield><subfield code="n">2507574</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-ocn182530762 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:16:12Z |
| institution | BVB |
| isbn | 9812565361 9789812565365 9812703152 9789812703156 1281899143 9781281899149 9786611899141 6611899146 |
| language | English |
| oclc_num | 182530762 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xiii, 373 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | World Scientific, |
| record_format | marc |
| spelling | Ramm, A. G. (Alexander G.) https://id.oclc.org/worldcat/entity/E39PBJht6c7MRHvFtQDQJ4MVmd http://id.loc.gov/authorities/names/n80129782 Random fields estimation / Alexander G. Ramm. Hackensack, NJ : World Scientific, ©2005. 1 online resource (xiii, 373 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier data file Includes bibliographical references (pages 363-369) and index. Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space. This book contains a novel theory of random fields estimation of Wiener type, developed originally by the author and presented here. No assumption about the Gaussian or Markovian nature of the fields are made. The theory, constructed entirely within the framework of covariance theory, is based on a detailed analytical study of a new class of multidimensional integral equations basic in estimation theory. This book is suitable for graduate courses in random fields estimation. It can also be used in courses in functional analysis, numerical analysis, integral equations, and scattering theory. Print version record. English. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Estimation theory. http://id.loc.gov/authorities/subjects/sh85044957 Champs aléatoires. Théorie de l'estimation. MATHEMATICS Probability & Statistics General. bisacsh Estimation theory fast Random fields fast Ramm, A. G. (Alexander G.). Random fields estimation theory. has work: Random fields estimation (Text) https://id.oclc.org/worldcat/entity/E39PCFrvXGMPFc44mGRdpGdjVK https://id.oclc.org/worldcat/ontology/hasWork Print version: Ramm, A.G. (Alexander G.). Random fields estimation. Hackensack, NJ : World Scientific, ©2005 (DLC) 2006299148 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=174689 Volltext |
| spellingShingle | Ramm, A. G. (Alexander G.) Random fields estimation / Cover -- Preface -- Contents -- 1. Introduction -- 2. Formulation of Basic Results -- 2.1 Statement of the problem -- 2.2 Formulation of the results (multidimensional case) -- 2.2.1 Basic results -- 2.2.2 Generalizations -- 2.3 Formulation of the results (one-dimensional case) -- 2.3.1 Basic results for the scalar equation -- 2.3.2 Vector equations -- 2.4 Examples of kernels of class R and solutions to the basic equation -- 2.5 Formula for the error of the optimal estimate -- 3. Numerical Solution of the Basic Integral Equation in Distributions -- 3.1 Basic ideas -- 3.2 Theoretical approaches -- 3.3 Multidimensional equation -- 3.4 Numerical solution based on the approximation of the kernel -- 3.5 Asymptotic behavior of the optimal filter as the white noise component goes to zero -- 3.6 A general approach -- 4. Proofs -- 4.1 Proof of Theorem 2.1 -- 4.2 Proof of Theorem 2.2 -- 4.3 Proof of Theorems 2.4 and 2.5 -- 4.4 Another approach -- 5. Singular Perturbation Theory for a Class of Fredholm Integral Equations Arising in Random Fields Estimation Theory -- 5.1 Introduction -- 5.2 Auxiliary results -- 5.3 Asymptotics in the case n = 1 -- 5.4 Examples of asymptotical solutions: case n = 1 -- 5.5 Asymptotics in the case n> 1 -- 5.6 Examples of asymptotical solutions: case n> 1 -- 6. Estimation and Scattering Theory -- 6.1 The direct scattering problem -- 6.1.1 The direct scattering problem -- 6.1.2 Properties of the scattering solution -- 6.1.3 Properties of the scattering amplitude -- 6.1.4 Analyticity in k of the scattering solution -- 6.1.5 High-frequency behavior of the scattering solutions -- 6.1.6 Fundamental relation between u+ and u- -- 6.1.7 Formula for det S (k) and state the Levinson Theorem -- 6.1.8 Completeness properties of the scattering solutions -- 6.2 Inverse scattering problems -- 6.2.1 Inverse scattering problems -- 6.2.2 Uniqueness theorem for the inverse scattering problem -- 6.2.3 Necessary conditions for a function to be a scatterng amplitude -- 6.2.4 A Marchenko equation (M equation) -- 6.2.5 Characterization of the scattering data in the 3D inverse scattering probtem -- 6.2.6 The Born inversion -- 6.3 Estimation theory and inverse scattering in R3 -- 7. Applications -- 7.1 What is the optimal size of the domain on which the data are to be collected? -- 7.2 Discrimination of random fields against noisy background -- 7.3 Quasioptimal estimates of derivatives of random functions -- 7.3.1 Introduction -- 7.3.2 Estimates of the derivatives -- 7.3.3 Derivatives of random functions -- 7.3.4 Finding critical points -- 7.3.5 Derivatives of random fields -- 7.4 Stable summation of orthogonal series and integrals with randomly perturbed coefficients -- 7.4.1 Introduction -- 7.4.2 Stable summation of series -- 7.4.3 Method of multipliers -- 7.5 Resolution ability of linear systems -- 7.5.1 Introduction -- 7.5.2 Resolution ability of linear systems -- 7.5.3 Optimization of resolution ability -- 7.5.4 A general definition of resolution ability -- 7.6 Ill-posed problems and estimation theory -- 7.6.1 Introduction -- 7.6.2 Stable solution of ill-posed problems -- 7.6.3 Equations with random noise -- 7.7 A remark on nonlinear (polynomial) estimates -- 8. Auxiliary Results -- 8.1 Sobolev spaces and distributions -- 8.1.1 A general imbedding theorem -- 8.1.2 Sobolev space. Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Estimation theory. http://id.loc.gov/authorities/subjects/sh85044957 Champs aléatoires. Théorie de l'estimation. MATHEMATICS Probability & Statistics General. bisacsh Estimation theory fast Random fields fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85111347 http://id.loc.gov/authorities/subjects/sh85044957 |
| title | Random fields estimation / |
| title_alt | Random fields estimation theory. |
| title_auth | Random fields estimation / |
| title_exact_search | Random fields estimation / |
| title_full | Random fields estimation / Alexander G. Ramm. |
| title_fullStr | Random fields estimation / Alexander G. Ramm. |
| title_full_unstemmed | Random fields estimation / Alexander G. Ramm. |
| title_short | Random fields estimation / |
| title_sort | random fields estimation |
| topic | Random fields. http://id.loc.gov/authorities/subjects/sh85111347 Estimation theory. http://id.loc.gov/authorities/subjects/sh85044957 Champs aléatoires. Théorie de l'estimation. MATHEMATICS Probability & Statistics General. bisacsh Estimation theory fast Random fields fast |
| topic_facet | Random fields. Estimation theory. Champs aléatoires. Théorie de l'estimation. MATHEMATICS Probability & Statistics General. Estimation theory Random fields |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=174689 |
| work_keys_str_mv | AT rammag randomfieldsestimation |