TY - BOOK
AU - Da Prato,Giuseppe
AU - Zabczyk,Jerzy
TI - Stochastic equations in infinite dimensions
T2 - Encyclopedia of mathematics and its applications
SN - 9781107088139
AV - QA274.25 .D4 1992eb
U1 - 519.2 22
PY - 1992///
CY - Cambridge, New York
PB - Cambridge University Press
KW - Stochastic partial differential equations
KW - Équations différentielles stochastiques
KW - Analyse stochastique
KW - Équations aux dérivées partielles stochastiques
KW - Semimartingales (Mathématiques)
KW - MATHEMATICS
KW - Applied
KW - bisacsh
KW - Probability & Statistics
KW - General
KW - fast
KW - Banach-Raum
KW - gnd
KW - Gleichung
KW - Hilbert-Raum
KW - Stochastik
KW - Equations aux dérivées partielles stochastiques
KW - ram
KW - Electronic books
N1 - 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
N2 - 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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ER -