# Stochastic equations in infinite dimensions /

Da Prato, Giuseppe.

Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk. - 1 online resource (xviii, 454 pages) - Encyclopedia of mathematics and its applications ; volume 45 [i.e. 44] . - Encyclopedia of mathematics and its applications ; volume 44. .

Includes bibliographical references (pages 427-449) and index.

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.

9781107088139 1107088135 9780511666223 0511666225

Stochastic partial differential equations.

Équations différentielles stochastiques.

Analyse stochastique.

Équations aux dérivées partielles stochastiques.

Semimartingales (Mathématiques)

MATHEMATICS--Applied.

MATHEMATICS--Probability & Statistics--General.

Stochastic partial differential equations.

Banach-Raum

Gleichung

Hilbert-Raum

Stochastik

Equations aux dérivées partielles stochastiques.

Electronic books.

Electronic books.

QA274.25 / .D4 1992eb

519.2

Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk. - 1 online resource (xviii, 454 pages) - Encyclopedia of mathematics and its applications ; volume 45 [i.e. 44] . - Encyclopedia of mathematics and its applications ; volume 44. .

Includes bibliographical references (pages 427-449) and index.

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.

9781107088139 1107088135 9780511666223 0511666225

Stochastic partial differential equations.

Équations différentielles stochastiques.

Analyse stochastique.

Équations aux dérivées partielles stochastiques.

Semimartingales (Mathématiques)

MATHEMATICS--Applied.

MATHEMATICS--Probability & Statistics--General.

Stochastic partial differential equations.

Banach-Raum

Gleichung

Hilbert-Raum

Stochastik

Equations aux dérivées partielles stochastiques.

Electronic books.

Electronic books.

QA274.25 / .D4 1992eb

519.2