Stochastic partial differential equations with Lévy noise : an evolution equation approach / S. Peszat and J. Zabczyk.

Format:

Book

Author/Creator:

Peszat, S., author.

Zabczyk, Jerzy, author.

Series:

Encyclopedia of mathematics and its applications ; v. 113.

Encyclopedia of mathematics and its applications ; volume 113

Language:

English

Subjects (All):

Stochastic partial differential equations.

Lévy processes.

Physical Description:

1 online resource (xii, 419 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

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 Lévy processes in infinite dimensions and their reproducing kernel Hilbert spaces; cylindrical Lévy 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.

Contents:

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

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

16. Invariant measures

17. Lattice systems

18. Stochastic Burgers equation

19. Environmental pollution model

20. Bond market models

App. A. Operators on Hilbert spaces

App. B. Co-semigroups

App. C. Regularization of Markov processes

App. D. Ito formulae

App. E. Levy-Khinchin formula on [0, + [infinity])

App. F. Proof of Lemma 4.24.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88343-7

1-107-10165-4

1-107-10408-4

1-107-09605-7

1-107-08975-1

0-511-72137-4