Stochastic equations in infinite dimensions:
The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, f...
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
1992
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications
volume 45 |
| Schlagworte: | |
| Online-Zugang: | BSB01 FHN01 Volltext |
| Zusammenfassung: | The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Beschreibung: | 1 online resource (xviii, 454 pages) |
| ISBN: | 9780511666223 |
| DOI: | 10.1017/CBO9780511666223 |
Internformat
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| 245 | 1 | 0 | |a Stochastic equations in infinite dimensions |c Giuseppe Da Prato, Jerzy Zabczyk |
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| 505 | 8 | |a Lifts of diffusion processes -- Random variables -- Probability measures -- Stochastic processes -- The stochastic integral -- Existence and uniqueness -- Linear equations with additive noise -- Linear equations with multiplicative noise -- Existence and uniqueness for nonlinear equations -- Martingale solutions -- Properties of solutions -- Markov properties and kolmogorov equations -- Absolute continuity and Girsanov's theorem -- Large time nehaviour of solutions -- Small noise noise asymptotic -- A linear deterministic equations -- Some results on control theory -- Nuclear and Hilbert, Schimidt operators -- Dissipative mappings | |
| 520 | |a The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Da Prato, Giuseppe |
| author_facet | Da Prato, Giuseppe |
| author_role | aut |
| author_sort | Da Prato, Giuseppe |
| author_variant | p g d pg pgd |
| building | Verbundindex |
| bvnumber | BV043941682 |
| classification_rvk | SK 820 |
| collection | ZDB-20-CBO |
| contents | Lifts of diffusion processes -- Random variables -- Probability measures -- Stochastic processes -- The stochastic integral -- Existence and uniqueness -- Linear equations with additive noise -- Linear equations with multiplicative noise -- Existence and uniqueness for nonlinear equations -- Martingale solutions -- Properties of solutions -- Markov properties and kolmogorov equations -- Absolute continuity and Girsanov's theorem -- Large time nehaviour of solutions -- Small noise noise asymptotic -- A linear deterministic equations -- Some results on control theory -- Nuclear and Hilbert, Schimidt operators -- Dissipative mappings |
| ctrlnum | (ZDB-20-CBO)CR9780511666223 (OCoLC)849793974 (DE-599)BVBBV043941682 |
| 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 |
| doi_str_mv | 10.1017/CBO9780511666223 |
| format | Electronic eBook |
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| id | DE-604.BV043941682 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511666223 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350652 |
| oclc_num | 849793974 |
| open_access_boolean | |
| owner | DE-12 DE-92 |
| owner_facet | DE-12 DE-92 |
| physical | 1 online resource (xviii, 454 pages) |
| psigel | ZDB-20-CBO ZDB-20-CBO BSB_PDA_CBO ZDB-20-CBO FHN_PDA_CBO |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Da Prato, Giuseppe Verfasser aut Stochastic equations in infinite dimensions Giuseppe Da Prato, Jerzy Zabczyk Cambridge Cambridge University Press 1992 1 online resource (xviii, 454 pages) txt rdacontent c rdamedia cr rdacarrier Encyclopedia of mathematics and its applications volume 45 Title from publisher's bibliographic system (viewed on 05 Oct 2015) Lifts of diffusion processes -- Random variables -- Probability measures -- Stochastic processes -- The stochastic integral -- Existence and uniqueness -- Linear equations with additive noise -- Linear equations with multiplicative noise -- Existence and uniqueness for nonlinear equations -- Martingale solutions -- Properties of solutions -- Markov properties and kolmogorov equations -- Absolute continuity and Girsanov's theorem -- Large time nehaviour of solutions -- Small noise noise asymptotic -- A linear deterministic equations -- Some results on control theory -- Nuclear and Hilbert, Schimidt operators -- Dissipative mappings The aim of this book is to give a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. These are a generalization of stochastic differential equations as introduced by Itô and Gikham that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations. The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measure on separable Banach and Hilbert spaces, as required later; they assume a reasonable background in probability theory and finite dimensional stochastic processes. The second part is devoted to the existence and uniqueness of solutions of a general stochastic evolution equation, and the third concerns the qualitative properties of those solutions. Appendices gather together background results from analysis that are otherwise hard to find under one roof. The book ends with a comprehensive bibliography that will contribute to the book's value for all working in stochastic differential equations Stochastic partial differential equations Unendlichdimensionaler Raum (DE-588)4207852-0 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 gnd rswk-swf Stochastische Differentialgleichung (DE-588)4057621-8 s Unendlichdimensionaler Raum (DE-588)4207852-0 s 1\p DE-604 Zabczyk, Jerzy Sonstige oth Erscheint auch als Druckausgabe 978-0-521-05980-0 Erscheint auch als Druckausgabe 978-0-521-38529-9 https://doi.org/10.1017/CBO9780511666223 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Da Prato, Giuseppe Stochastic equations in infinite dimensions Lifts of diffusion processes -- Random variables -- Probability measures -- Stochastic processes -- The stochastic integral -- Existence and uniqueness -- Linear equations with additive noise -- Linear equations with multiplicative noise -- Existence and uniqueness for nonlinear equations -- Martingale solutions -- Properties of solutions -- Markov properties and kolmogorov equations -- Absolute continuity and Girsanov's theorem -- Large time nehaviour of solutions -- Small noise noise asymptotic -- A linear deterministic equations -- Some results on control theory -- Nuclear and Hilbert, Schimidt operators -- Dissipative mappings Stochastic partial differential equations Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| subject_GND | (DE-588)4207852-0 (DE-588)4057621-8 |
| title | Stochastic equations in infinite dimensions |
| title_auth | Stochastic equations in infinite dimensions |
| title_exact_search | Stochastic equations in infinite dimensions |
| title_full | Stochastic equations in infinite dimensions Giuseppe Da Prato, Jerzy Zabczyk |
| title_fullStr | Stochastic equations in infinite dimensions Giuseppe Da Prato, Jerzy Zabczyk |
| title_full_unstemmed | Stochastic equations in infinite dimensions Giuseppe Da Prato, Jerzy Zabczyk |
| title_short | Stochastic equations in infinite dimensions |
| title_sort | stochastic equations in infinite dimensions |
| topic | Stochastic partial differential equations Unendlichdimensionaler Raum (DE-588)4207852-0 gnd Stochastische Differentialgleichung (DE-588)4057621-8 gnd |
| topic_facet | Stochastic partial differential equations Unendlichdimensionaler Raum Stochastische Differentialgleichung |
| url | https://doi.org/10.1017/CBO9780511666223 |
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