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Numerical Methods for Stochastic Simulation: When Stochastic Integration Meets Geometric Numerical Integration

In: Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology

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  • Assyr Abdulle

    (Institut de Mathmatiques, École Polytechnique Fédérale de Lausanne, ANMC)

Abstract

In this paper we discuss a framework recently introduced to construct and analyze accurate stochastic integrators for the computation of expectation of functionals of a stochastic process for both finite time or long-time dynamics. Such accurate integrators are of interest for many applications in biology, chemistry or physics and are also often needed in multiscale stochastic simulations. We describe how ideas originating from geometric numerical integration or structure preserving methods for deterministic differential equations can help to design new integrators for weak approximation of stochastic differential equations or for long-time simulation of ergodic stochastic systems.

Suggested Citation

  • Assyr Abdulle, 2017. "Numerical Methods for Stochastic Simulation: When Stochastic Integration Meets Geometric Numerical Integration," Springer Books, in: David Holcman (ed.), Stochastic Processes, Multiscale Modeling, and Numerical Methods for Computational Cellular Biology, pages 83-107, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-62627-7_4
    DOI: 10.1007/978-3-319-62627-7_4
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