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,...
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York :
Cambridge University Press,
1992.
|
| Schriftenreihe: | Encyclopedia of mathematics and its applications ;
volume 44. |
| Schlagworte: | |
| Online-Zugang: | 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: | 1 online resource (xviii, 454 pages) |
| Bibliographie: | Includes bibliographical references (pages 427-449) and index. |
| ISBN: | 9781107088139 1107088135 9780511666223 0511666225 |
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| 245 | 1 | 0 | |a Stochastic equations in infinite dimensions / |c Giuseppe Da Prato, Jerzy Zabczyk. |
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| 505 | 0 | |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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| 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. |
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| discipline | Mathematik |
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| genre | Electronic book. |
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| id | ZDB-4-EBA-ocn861692162 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:25:36Z |
| institution | BVB |
| isbn | 9781107088139 1107088135 9780511666223 0511666225 |
| language | English |
| oclc_num | 861692162 |
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| physical | 1 online resource (xviii, 454 pages) |
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| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Cambridge University Press, |
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| series | Encyclopedia of mathematics and its applications ; |
| series2 | Encyclopedia of mathematics and its applications ; |
| spelling | Da Prato, Giuseppe. Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk. Cambridge ; New York : Cambridge University Press, 1992. 1 online resource (xviii, 454 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of mathematics and its applications ; volume 45 [i.e. 44] Includes bibliographical references (pages 427-449) and index. Print version record. 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. http://id.loc.gov/authorities/subjects/sh87001697 Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Semimartingales (Mathematics) http://id.loc.gov/authorities/subjects/sh87002402 Équations différentielles stochastiques. Analyse stochastique. Équations aux dérivées partielles stochastiques. Semi-martingales (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic analysis fast Semimartingales (Mathematics) fast Stochastic partial differential equations fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Gleichung gnd http://d-nb.info/gnd/4021246-4 Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Stochastik gnd http://d-nb.info/gnd/4121729-9 Equations aux dérivées partielles stochastiques. ram Electronic book. Zabczyk, Jerzy. Print version: Da Prato, Giuseppe. Stochastic equations in infinite dimensions 0521385296 (DLC) 93118317 (OCoLC)27768406 Encyclopedia of mathematics and its applications ; volume 44. http://id.loc.gov/authorities/names/n42010632 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569300 Volltext |
| spellingShingle | Da Prato, Giuseppe Stochastic equations in infinite dimensions / Encyclopedia of mathematics and its applications ; 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. http://id.loc.gov/authorities/subjects/sh87001697 Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Semimartingales (Mathematics) http://id.loc.gov/authorities/subjects/sh87002402 Équations différentielles stochastiques. Analyse stochastique. Équations aux dérivées partielles stochastiques. Semi-martingales (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic analysis fast Semimartingales (Mathematics) fast Stochastic partial differential equations fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Gleichung gnd http://d-nb.info/gnd/4021246-4 Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Stochastik gnd http://d-nb.info/gnd/4121729-9 Equations aux dérivées partielles stochastiques. ram |
| subject_GND | http://id.loc.gov/authorities/subjects/sh87001697 http://id.loc.gov/authorities/subjects/sh85128177 http://id.loc.gov/authorities/subjects/sh85128175 http://id.loc.gov/authorities/subjects/sh87002402 http://d-nb.info/gnd/4004402-6 http://d-nb.info/gnd/4021246-4 http://d-nb.info/gnd/4159850-7 http://d-nb.info/gnd/4121729-9 |
| 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. http://id.loc.gov/authorities/subjects/sh87001697 Stochastic differential equations. http://id.loc.gov/authorities/subjects/sh85128177 Stochastic analysis. http://id.loc.gov/authorities/subjects/sh85128175 Semimartingales (Mathematics) http://id.loc.gov/authorities/subjects/sh87002402 Équations différentielles stochastiques. Analyse stochastique. Équations aux dérivées partielles stochastiques. Semi-martingales (Mathématiques) MATHEMATICS Applied. bisacsh MATHEMATICS Probability & Statistics General. bisacsh Stochastic differential equations fast Stochastic analysis fast Semimartingales (Mathematics) fast Stochastic partial differential equations fast Banach-Raum gnd http://d-nb.info/gnd/4004402-6 Gleichung gnd http://d-nb.info/gnd/4021246-4 Hilbert-Raum gnd http://d-nb.info/gnd/4159850-7 Stochastik gnd http://d-nb.info/gnd/4121729-9 Equations aux dérivées partielles stochastiques. ram |
| topic_facet | Stochastic partial differential equations. Stochastic differential equations. Stochastic analysis. Semimartingales (Mathematics) Équations différentielles stochastiques. Analyse stochastique. Équations aux dérivées partielles stochastiques. Semi-martingales (Mathématiques) MATHEMATICS Applied. MATHEMATICS Probability & Statistics General. Stochastic differential equations Stochastic analysis Stochastic partial differential equations Banach-Raum Gleichung Hilbert-Raum Stochastik Equations aux dérivées partielles stochastiques. Electronic book. |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=569300 |
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