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Convergence of a stochastic particle approximation for fractional scalar conservation laws

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  • Jourdain, Benjamin
  • Roux, Raphaël
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    Abstract

    We are interested in a probabilistic approximation of the solution to scalar conservation laws with fractional diffusion and nonlinear drift. The probabilistic interpretation of this equation is based on a stochastic differential equation driven by an [alpha]-stable Lévy process and involving a nonlinear drift. The approximation is constructed using a system of particles following a time-discretized version of this stochastic differential equation, with nonlinearity replaced by interaction. We prove convergence of the particle approximation to the solution of the conservation law as the number of particles tends to infinity whereas the discretization step tends to 0 in some precise asymptotics.

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    Bibliographic Info

    Article provided by Elsevier in its journal Stochastic Processes and their Applications.

    Volume (Year): 121 (2011)
    Issue (Month): 5 (May)
    Pages: 957-988

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    Handle: RePEc:eee:spapps:v:121:y:2011:i:5:p:957-988

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    Related research

    Keywords: Nonlinear partial differential equations Interacting particle systems Euler scheme [alpha]-stable Lévy processes;

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    Cited by:
    1. Vassili Kolokoltsov & Marianna Troeva & Wei Yang, 2014. "On the Rate of Convergence for the Mean-Field Approximation of Controlled Diffusions with Large Number of Players," Dynamic Games and Applications, Springer, vol. 4(2), pages 208-230, June.

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