Stochastic partial differential equations with Lévy noise : an evolution equation approach

著者

• Peszat, S.
• Zabczyk, Jerzy

書誌事項

Stochastic partial differential equations with Lévy noise : an evolution equation approach

S. Peszat and J. Zabczyk

（Encyclopedia of mathematics and its applications / edited by G.-C. Rota, [113]）

Cambridge University Press, 2007

• : hbk

注記

Includes bibliographical references (p. 403-414) and index

"Encyclopedia of mathematics and its applications 113"--Jaceket

内容説明・目次

内容説明

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.

目次

• 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.

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詳細情報

• NII書誌ID(NCID): BA83380591
• ISBN:
  • 9780521879897
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge ; New York
• ページ数/冊数: xii, 419 p.
• 大きさ: 25 cm
• 親書誌ID:
  • BA00064663