Stochastic Equations in Infinite Dimensions

Giuseppe Da Prato is Emeritus Professor at the Scuola Normale Superiore di Pisa. His research activity concerns: stochastic analysis, evolution equations both deterministic and stochastic, elliptic and parabolic equations with infinitely many variables, deterministic and stochastic control. On these subjects he has produced more than 350 papers in reviewed journals and eight books. Jerzy Zabczyk is Professor in the Institute of Mathematics at the Polish Academy of Sciences. His research interests include stochastic processes, evolution equations, control theory and mathematical finance. He has published 87 papers in mathematical journals and seven books.

• 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.

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