Stochastic equations in infinite dimensions / Giuseppe Da Prato, Jerzy Zabczyk.

Format:

Book

Author/Creator:

Da Prato, Giuseppe, author.

Zabczyk, Jerzy, author.

Series:

Encyclopedia of mathematics and its applications ; v. 45.

Encyclopedia of mathematics and its applications ; volume 45

Language:

English

Subjects (All):

Stochastic partial differential equations.

Physical Description:

1 online resource (xviii, 454 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1992.

Language Note:

English

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 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.

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.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88453-0

0-511-95022-5

1-107-10275-8

1-107-09428-3

1-107-08813-5

0-511-66622-5