Stochastic Partial Differential Equations with Lévy Noise

Szymon Peszat is an Associate Professor in the Institute of Mathematics at the Polish Academy of Sciences. Jerzy Zabczyk is a Professor in the Institute of Mathematics at the Polish Academy of Sciences. He is the author (with G. Da Prato) of three earlier books for Cambridge University Press: Stochastic Equations in Infinite Dimensions (1992), Ergodicity for Infinite Dimensional Systems (1996) and Second Order Partial Differential Equations (2002).

• Introduction; Part I. Foundations: 1. Why equations with Lévy noise?; 2. Analytic preliminaries; 3. Probabilistic preliminaries; 4. Lévy processes; 5. Lévy semigroups; 6. Poisson random measures; 7. Cylindrical processes and reproducing kernels; 8. Stochastic integration; Part II. Existence and Regularity: 9. General existence and uniqueness results; 10. Equations with non-Lipschitz coefficients; 11. Factorization and regularity; 12. Stochastic parabolic problems; 13. Wave and delay equations; 14. Equations driven by a spatially homogeneous noise; 15. Equations with noise on the boundary; Part III. Applications: 16. Invariant measures; 17. Lattice systems; 18. Stochastic Burgers equation; 19. Environmental pollution model; 20. Bond market models; Appendix 1. Operators on Hilbert spaces; Appendix 2. C0-semigroups; Appendix 3. Regularization of Markov processes; Appendix 4. Itô formulae; Appendix 5. Lévy-Khinchin on [0,+ ); Appendix 6. Proof of Lemma; List of symbols; Bibliography; Index.

'Summarising, this book is an excellent addition to the literature on stochastic partial differential equations in general and in particular with respect to evolution equations driven by a discontinuous noise. The exposition is self-contained and very well written and, in my opinion, will become a standard tool for everyone working on stochastic evolution equations and related areas.' Zentralblatt MATH