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Stochastic Partial Differential Equations with Lévy Noise

Stochastic Partial Differential Equations with Lévy Noise
An Evolution Equation Approach


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: October 2007
  • availability: Available
  • format: Hardback
  • isbn: 9780521879897

£ 126.00

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About the Authors
  • 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.

    • Was the first book to detail the evolution equation approach to the solution of stochastic partial differential equations with Lévy noise
    • Rapidly growing topic - majority of results appear here for the first time
    • Great potential for applications to finance, statistical mechanics and fluid dynamics
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    Reviews & endorsements

    '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

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    Product details

    • Date Published: October 2007
    • format: Hardback
    • isbn: 9780521879897
    • length: 432 pages
    • dimensions: 235 x 165 x 29 mm
    • weight: 0.78kg
    • availability: Available
  • Table of Contents

    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

  • Authors

    S. Peszat, Polish Academy of Sciences
    Szymon Peszat is an Associate Professor in the Institute of Mathematics at the Polish Academy of Sciences.

    J. Zabczyk, 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).

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