Stochastic equations in infinite dimensions
著者
書誌事項
Stochastic equations in infinite dimensions
（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, 45）
Cambridge University Press, 2008, c1992
- : pbk.
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注記
Includes bibliography (p. 427-449) and index
"This digitally printed version (with corrections) 2008" -- T.p. verso
First published 1992
内容説明・目次
内容説明
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 Ito 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.
目次
- Part I. Foundations: 1. Random variables
- 2. Probability measures
- 3. Stochastic processes
- 4. The stochastic integral
- Part II. Existence and Uniqueness: 5. Linear equations with additive noise
- 6. Linear equations with multiplicative noise
- 7. Existence and uniqueness for nonlinear equations
- 8. Martingale solutions
- Part III. Properties of Solutions: 9. Markov properties and Kolmogorov equations
- 10. Absolute continuity and Girsanov's theorem
- 11. Large time behaviour of solutions
- 12. Small noise asymptotic.
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