Stochastic Partial Differential Equations with Lévy Noise: An Evolution Equation Approach

ISBN-13: 9780521879897 / Angielski / Twarda / 2007 / 432 str.

S Peszat

Opis

Recent years have seen an explosion of interest in stochastic partial differential equations where the driving noise is discontinuous. In this comprehensive monograph, two leading experts detail the evolution equation approach to their solution. Most of the results appeared here for the first time in book form. The authors start with a detailed analysis of Levy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Levy processes are constructed in terms of Poisson random measures; stochastic integrals are introduced. Stochastic parabolic and hyperbolic equations on domains of arbitrary dimensions are studied, and applications to statistical and fluid mechanics and to finance are also investigated. Ideal for researchers and graduate students in stochastic processes and partial differential equations, this self-contained text will also interest those working on stochastic modeling in finance, statistical physics and environmental science."

Recenzje

'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

Spis treści

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.