Probabilistic Approximation via Spatial Derivation of Some Nonlinear Parabolic Evolution Equations

B. Jourdain ()
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B. Jourdain: ENPC-CERMICS

A chapter in Monte Carlo and Quasi-Monte Carlo Methods 2004, 2006, pp 197-216 from Springer

Abstract: 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.

Keywords: Weak Solution; Empirical Measure; Probabilistic Interpretation; Nonlinear Parabolic Equation; Unique Weak Solution (search for similar items in EconPapers)
Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-31186-7_13

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DOI: 10.1007/3-540-31186-6_13

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