Random fields and stochastic partial differential equations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer
1998
|
| Schriftenreihe: | Mathematics and its applications
438 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VII, 229 S. Ill. |
| ISBN: | 0792349849 9780792349846 |
Internformat
MARC
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| 100 | 1 | |a Rozanov, Jurij A. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Random fields and stochastic partial differential equations |c by Yu. A. Rozanov |
| 264 | 1 | |a Dordrecht [u.a.] |b Kluwer |c 1998 | |
| 300 | |a VII, 229 S. |b Ill. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Mathematics and its applications |v 438 | |
| 650 | 0 | 7 | |a Zufälliges Feld |0 (DE-588)4191094-1 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Stochastische partielle Differentialgleichung |0 (DE-588)4135969-0 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Stochastische partielle Differentialgleichung |0 (DE-588)4135969-0 |D s |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-008142866 | ||
Datensatz im Suchindex
| _version_ | 1804126628115120128 |
|---|---|
| adam_text | CONTENTS
Foreword 1
Chapter I. Random Fields and Stochastic
Sobolev Spaces 5
1.1. Generalized random fields 5
1.1. Introductionary concept 5
1.2. Stochastic integral representations 8
1.3. Generalized random fields with independent values 12
1.2. Random fields realizations 16
2.1. Some embeddings 16
2.2. Gaussian random fields 18
1.3. Test functions spaces 20
3.1. Spaces of the W type 20
3.2. The Fourier transform of VF spaces 26
3.3. The equivalent Sobolev spaces 32
3.4. Multiplicators and localization of generalized functions . 39
1.4. The Sobolev spaces 44
4.1. Some point wise properties of generalized derivatives .. .44
4.2. Test functions spaces 49
4.3. Boundary test functions 52
4.4. Anisotropic Sobolev spaces 63
4.5. Dual Sobolev spaces 68
4.6. Hilbert Schmidt embeddings 70
1.5. Generalized random functions and stochastic
Sobolev spaces 72
5.1. Random Schwartz distributions 72
5.2. Stochastic Sobolev spaces 75
5.3. Stochastic Dirichlet problem 80
vi CONTENTS
Chapter II. Equations for Generalized Random
Functions 85
II. 1. Generalized Differential Equations 85
1.1. Test functions for generalized differential equations 85
1.2. Generalized differential equations for some probability
functional models 92
11.2. Boundary conditions for generalized differential equations 104
2.1. Solvability of the equations 104
2.2. Boundary test functions 106
2.3. General boundary conditions Ill
2.4. Stochastic generalized ordinary differential equations . 119
11.3. Boundary conditions for some random fields models 124
3.1. Stochastic string equation 124
3.2. Stochastic Laplace equation 134
11.4. Boundary Conditions for Stochastic
Evolution Equations 138
4.1. Preliminaries 138
4.2. Semigroup approach to deterministic equations4 146
4.3. Stochastic equations5 150
11.5. Homogeneous Equations 152
5.1. General solution and its approximations 152
5.2. Hyperellipticity, extension of solutions, and negligible
singularities 156
5.3. Limit of solutions in regions with increasingly
complicated structure 160
Chapter III. Random Fields Associated ¦with Partial
Equations 167
111.1. Some Characteristics of Probability 167
1.1. Mean values and correlations 167
1.2. Characteristic functional 170
111.2. Forecast and Global Markov Property 172
2.1. Forecast problem 172
2.2. Global Markov Property 181
111.3. A Generalized Approach to Boundary Problems 187
Chapter IV. Gaussian Random Fields 193
IV. 1. Some General Properties 193
1.1. Gaussian random variables and a algebras of
events 193
1.2. Polynomials of Gaussian random variables 196
CONTENTS vii
1.3. Comparison theorem for quadratic forms of
Gaussian random variables 199
1.4. The likelihood ratio 201
IV.2. Identification of Stochastic Differential Equations 207
2.1. Equivalence conditions and singularity of Gaussian
distributions 207
2.2. Identification of coefficients 211
2.3. On the likelyhood ratio 217
IV.3. Estimation of Mean Value in Stochastic Differential
Equations 219
3.1. The best unbiased estimators 219
3.2. Pseudo best estimators, the method of east squares,
and the consistency condition 225
|
| any_adam_object | 1 |
| author | Rozanov, Jurij A. |
| author_facet | Rozanov, Jurij A. |
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| author_sort | Rozanov, Jurij A. |
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| building | Verbundindex |
| bvnumber | BV012033680 |
| classification_rvk | SK 820 |
| ctrlnum | (OCoLC)246725310 (DE-599)BVBBV012033680 |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV012033680 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:20:28Z |
| institution | BVB |
| isbn | 0792349849 9780792349846 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008142866 |
| oclc_num | 246725310 |
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| owner | DE-739 DE-703 DE-355 DE-BY-UBR DE-83 |
| owner_facet | DE-739 DE-703 DE-355 DE-BY-UBR DE-83 |
| physical | VII, 229 S. Ill. |
| publishDate | 1998 |
| publishDateSearch | 1998 |
| publishDateSort | 1998 |
| publisher | Kluwer |
| record_format | marc |
| series | Mathematics and its applications |
| series2 | Mathematics and its applications |
| spelling | Rozanov, Jurij A. Verfasser aut Random fields and stochastic partial differential equations by Yu. A. Rozanov Dordrecht [u.a.] Kluwer 1998 VII, 229 S. Ill. txt rdacontent n rdamedia nc rdacarrier Mathematics and its applications 438 Zufälliges Feld (DE-588)4191094-1 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd rswk-swf Stochastische partielle Differentialgleichung (DE-588)4135969-0 s Zufälliges Feld (DE-588)4191094-1 s DE-604 Mathematics and its applications 438 (DE-604)BV008163334 438 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008142866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Rozanov, Jurij A. Random fields and stochastic partial differential equations Mathematics and its applications Zufälliges Feld (DE-588)4191094-1 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| subject_GND | (DE-588)4191094-1 (DE-588)4135969-0 |
| title | Random fields and stochastic partial differential equations |
| title_auth | Random fields and stochastic partial differential equations |
| title_exact_search | Random fields and stochastic partial differential equations |
| title_full | Random fields and stochastic partial differential equations by Yu. A. Rozanov |
| title_fullStr | Random fields and stochastic partial differential equations by Yu. A. Rozanov |
| title_full_unstemmed | Random fields and stochastic partial differential equations by Yu. A. Rozanov |
| title_short | Random fields and stochastic partial differential equations |
| title_sort | random fields and stochastic partial differential equations |
| topic | Zufälliges Feld (DE-588)4191094-1 gnd Stochastische partielle Differentialgleichung (DE-588)4135969-0 gnd |
| topic_facet | Zufälliges Feld Stochastische partielle Differentialgleichung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008142866&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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