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 generalisation of stochastic differential equations as introduced by Ito and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations."--BOOK JACKET. "The book is divided into three parts. In th…
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- Full title :Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk.
Summary
"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 generalisation of stochastic differential equations as introduced by Ito and Gikhman that occur, for instance, when describing random phenomena that crop up in science and engineering, as well as in the study of differential equations."--BOOK JACKET. "The book is divided into three parts. In the first the authors give a self-contained exposition of the basic properties of probability measures 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."--Jacket.
Read More ↓Edition Statements
- Publication Date:1992.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge
- Language:eng
- Publication Date:1992.
The Physical Object
- Description:xviii, 454 pages ; : 24 cm.
Edition Identifiers
- ISBN:0521385296, 9780521385299, 9780521059800, 0521059801
- oclc:ocm27768406
- LC Classification:QA274.25
- Dewey Decimal:519.2
Table of 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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