Stochastic Equations in Infinite Dimensions: 152 (Encyclopedia of Mathematics and its Applications, Series Number 152)
Cambridge University Press
Edition: 2, 4/17/2014
EAN 9781107055841, ISBN10: 1107055849
Hardcover, 512 pages, 23.4 x 15.6 x 2.9 cm
Language: English
Originally published in English
Now 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.
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.