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Taylor Approximations for Stochastic Partial Differential Equations

Taylor Approximations for Stochastic Partial Differential Equations

£59.00

Part of CBMS-NSF Regional Conference Series in Applied Mathematics

  • Date Published: December 2011
  • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • format: Paperback
  • isbn: 9781611972009

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About the Authors
  • This book presents a systematic theory of Taylor expansions of evolutionary-type stochastic partial differential equations (SPDEs). The authors show how Taylor expansions can be used to derive higher order numerical methods for SPDEs, with a focus on pathwise and strong convergence. In the case of multiplicative noise, the driving noise process is assumed to be a cylindrical Wiener process, while in the case of additive noise the SPDE is assumed to be driven by an arbitrary stochastic process with Hölder continuous sample paths. Recent developments on numerical methods for random and stochastic ordinary differential equations are also included since these are relevant for solving spatially discretised SPDEs as well as of interest in their own right. The authors include the proof of an existence and uniqueness theorem under general assumptions on the coefficients as well as regularity estimates in an appendix.

    • Provides the reader with access to a rapidly developing field that will be widely applied in future years
    • A rich source of information for those interested in using and further developing numerical methods for stochastic partial differential equations
    • Suitable as source material for graduate courses
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    Product details

    • Date Published: December 2011
    • format: Paperback
    • isbn: 9781611972009
    • length: 235 pages
    • dimensions: 250 x 172 x 13 mm
    • weight: 0.39kg
    • availability: This item is not supplied by Cambridge University Press in your region. Please contact Soc for Industrial null Mathematics for availability.
  • Table of Contents

    Preface
    List of figures
    1. Introduction
    Part I. Random and Stochastic Ordinary Partial Differential Equations:
    2. RODEs
    3. SODEs
    4. SODEs with nonstandard assumptions
    Part II. Stochastic Partial Differential Equations:
    5. SPDEs
    6. Numerical methods for SPDEs
    7. Taylor approximations for SPDEs with additive noise
    8. Taylor approximations for SPDEs with multiplicative noise
    Appendix: regularity estimates for SPDEs
    Bibliography
    Index.

  • Authors

    Arnulf Jentzen, Princeton University, New Jersey
    Arnulf Jentzen is appointed as a Visiting Fellow in the Department of Applied and Computational Mathematics at Princeton University. His research focuses on analytical and numerical aspects of stochastic differential equations with non-globally Lipschitz continuous nonlinearities.

    Peter Kloeden, Goethe-Universität Frankfurt am Main
    Peter E. Kloeden is a Professor of Applied and Instrumental Mathematics at Goethe University, Frankfurt am Main. He is a Fellow both of SIAM and of the Australian Mathematical Society. He was awarded the W. T. and Idalia Reid Prize in Mathematics by SIAM in 2006 for his fundamental contributions to the theoretical and computational analysis of differential equations.

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