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Probabilistic Approximation via Spatial Derivation of Some Nonlinear Parabolic Evolution Equations

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Monte Carlo and Quasi-Monte Carlo Methods 2004

Summary

For some parabolic equations with a local nonlinearity, a suitable spatial derivation leads to a Fokker-Planck equation with a nonlocal nonlinearity. In this paper we present a review of the particle methods obtained by replacing the nonlinearity in this Fokker-Planck equation by interaction. We are interested in the convergence results for the particle approximations of the original equations and give the milestones of their proofs.

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Author information

Authors and Affiliations

  1. ENPC-CERMICS, 6-8 av Blaise Pascal, Cité Descartes, Champs sur Marne, 77455, Marne-la-Vallée Cedex 2, France

    B. Jourdain

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  1. B. Jourdain
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Editor information

Editors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Republic of Singapore

    Harald Niederreiter

  2. INRIA Sophia Antipolis, route des lucioles 2004, 06902, Sophia Antipolis Cedex, France

    Denis Talay

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Jourdain, B. (2006). Probabilistic Approximation via Spatial Derivation of Some Nonlinear Parabolic Evolution Equations. In: Niederreiter, H., Talay, D. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2004. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-31186-6_13

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