Stochastic equations in infinite dimensions / Giuseppe Da Prato and Jerzy Zabczyk.

Includes bibliographical references (pages 446-490) and index.

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;
13. Survey of specific equations;
14. Some recent de4velopments;
Appendices;
Bibliography;
Index.

"Now in its second edition, this book gives a systematic and self-contained presentation of basic results on stochastic evolution equations in infinite dimensional spaces, typically Hilbert and Banach spaces. In the first part the authors give an exposition of the main 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. This revised edition includes two brand new chapters surveying recent developments in the field and an even more comprehensive bibliography, making this book an essential and up-to-date resource for all those working in stochastic differential equations"--