Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations

Abstract : We introduce a new class of nonlinear Stochastic Differential Equations in the sense of McKean, related to non conservative nonlinear Partial Differential equations (PDEs). We discuss existence and uniqueness pathwise and in law under various assumptions. We propose an original interacting particle system for which we discuss the propagation of chaos. To this system, we associate a random function which is proved to converge to a solution of a regularized version of PDE.
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https://hal-ensta-paris.archives-ouvertes.fr//hal-01142337
Contributor : Francesco Russo <>
Submitted on : Wednesday, April 15, 2015 - 7:19:55 AM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM
Long-term archiving on : Monday, September 14, 2015 - 8:51:43 AM

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  • HAL Id : hal-01142337, version 1
  • ARXIV : 1504.03882

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Anthony Lecavil, Nadia Oudjane, Francesco Russo. Probabilistic representation of a class of non conservative nonlinear Partial Differential Equations. 2015. ⟨hal-01142337⟩

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