Stochastic Equations in Infinite Dimensions
Stochastic Equations in Infinite Dimensions
$180.00
USDNow in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional, typically Hilbert and Banach, spaces. In the first part 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. This revised edition includes two brand new chapters surveying recent developments in the area and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations.
- Thoroughly updated to reflect changes since publication of the first edition
- Provides a solid foundation to the whole theory of stochastic evolution equations
- Useful starting point for further research
Reviews & endorsements
Review of the first edition: 'The exposition is excellent and readable throughout, and should help bring the theory to a wider audience.' Daniel L. Ocone, Stochastics and Stochastic Reports
Review of the first edition: '… a welcome contribution to the rather new area of infinite dimensional stochastic evolution equations, which is far from being complete, so it should provide both a useful background and motivation for further research.' Yuri Kifer, The Annals of Probability
Review of the first edition: '… an excellent book which covers a large part of stochastic evolution equations with clear proofs and a very interesting analysis of their properties … In my opinion this book will become an indispensable tool for everybody working on stochastic evolution equations and related areas.' P. Kotelenez, American Mathematical Society
Product details
April 2014Adobe eBook Reader
9781139899598
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- Introduction
- Part I. Foundations:
- 1. Random variables
- 2. Probability measures
- 3. Stochastic processes
- 4. 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
- 9. Markov property and Kolmogorov equation
- 10. Absolute continuity and Girsanov theorem
- 11. Large time behavior of solutions
- 12. Small noise asymptotic
- 13. Survey of specific equations
- 14. Some recent developments
- Appendix A. Linear deterministic equations
- Appendix B. Some results on control theory
- Appendix C. Nuclear and Hilbert–Schmidt operators
- Appendix D. Dissipative mappings
- Bibliography
- Index.
