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By Guiseppe Da Prato
By Jerzy Zabczyk
Publisher: Cambridge University Press
Print Publication Year:1992
Online Publication Date:March 2010
Online ISBN:9780511666223
Hardback ISBN:9780521385299
Paperback ISBN:9780521059800
Book DOI: http://dx.doi.org/10.1017/CBO9780511666223
Subjects: Probability Theory and Stochastic Processes , Differential and Integral Equations, Dynamical Systems and Control Theory
The aim of this book is to give a systematic and self-contained presentation of the 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 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. 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.
Reviews:
pp. i-vi
pp. vii-xii
pp. xiii-xviii
Introduction: Motivating examples: Read PDF
pp. 1-12
pp. 13-14
1 - Random Variables: Read PDF
pp. 15-29
2 - Probability measures: Read PDF
pp. 30-69
3 - Stochastic processes: Read PDF
pp. 70-85
4 - The stochastic integral: Read PDF
pp. 86-114
II - Existence and Uniqueness: Read PDF
pp. 115-116
5 - Linear equations with additive noise: Read PDF
pp. 117-149
6 - Linear equations with multiplicative noise: Read PDF
pp. 150-179
7 - Existence and uniqueness for nonlinear equations: Read PDF
pp. 180-217
8 - Martingale solutions: Read PDF
pp. 218-236
III - Properties of solutions: Read PDF
pp. 237-238
9 - Markov properties and Kolmogorov equations: Read PDF
pp. 239-277
10 - Absolute continuity and Girsanov's theorem: Read PDF
pp. 278-301
11 - Large time behaviour of solutions: Read PDF
pp. 302-345
12 - Small noise asymptotic: Read PDF
pp. 346-378
A - Linear deterministic equations: Read PDF
pp. 379-405
B - Some results on control theory: Read PDF
pp. 406-414
C - Nuclear and Hilbert - Schmidt operators: Read PDF
pp. 415-419
D - Dissipative mappings: Read PDF
pp. 420-426
pp. 427-450
pp. 451-454