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Particle system algorithm and chaos propagation related to non-conservative McKean type stochastic differential equations

  • Anthony Le Cavil
  • Nadia Oudjane
  • Francesco Russo
Article
  • 81 Downloads

Abstract

We discuss numerical aspects related to a new class of NonLinear Stochastic Differential Equation (NLSDE) in the sense of McKean, which are supposed to represent non conservative nonlinear Partial Differential Equations (PDEs). We propose an original interacting particle system for which we discuss the propagation of chaos. We consider a time-discretized approximation of this particle system to which we associate a random function which is proved to converge to a solution of a regularized version of a nonlinear PDE.

Keywords

Chaos propagation Nonlinear Partial Differential Equations McKean type NonLinear Stochastic Differential Equation Particle systems Probabilistic representation of PDEs 

Mathematics Subject Classification

65C05 65C35 68U20 60H10 60H30 60J60 58J35 

Notes

Acknowledgments

The authors are very grateful to the anonymous Referee for her/his careful reading of the paper and the suggestions which have largely contributed to improve the first submitted version. The third named author has benefited partially from the support of the “FMJH Program Gaspard Monge in optimization and operation research” (Project 2014-1607H).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Anthony Le Cavil
    • 1
  • Nadia Oudjane
    • 2
  • Francesco Russo
    • 1
  1. 1.ENSTA-ParisTech, Université Paris-Saclay, Unité de Mathématiques Appliquées (UMA)PalaiseauFrance
  2. 2.EDF R&D, and FiME (Laboratoire de Finance des Marchés de l’Energie (Dauphine, CREST, EDF R&D))Clamart CedexFrance

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