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

ISBN: 9781139239370 出版年：2007 页码：434 S Peszat J Zabczyk Cambridge University Press

Introduction Part I. Foundations: 1. Why equations with Levy noise? 2. Analytic preliminaries 3. Probabilistic preliminaries 4. Levy processes 5. Levy 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. Ito formulae Appendix 5. Levy-Khinchin on [0,+ ) Appendix 6. Proof of Lemma List of symbols Bibliography Index.