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McKean Feynman-Kac probabilistic representations of non-linear partial differential equations

Abstract : This paper presents a partial state of the art about the topic of representation of generalized Fokker-Planck Partial Differential Equations (PDEs) by solutions of McKean Feynman-Kac Equations (MFKEs) that generalize the notion of McKean Stochastic Differential Equations (MSDEs). While MSDEs can be related to non-linear Fokker-Planck PDEs, MFKEs can be related to non-conservative non-linear PDEs. Motivations come from modeling issues but also from numerical approximation issues in computing the solution of a PDE, arising for instance in the context of stochastic control. MFKEs also appear naturally in representing final value problems related to backward Fokker-Planck equations.
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Submitted on : Friday, December 6, 2019 - 12:56:12 PM
Last modification on : Friday, December 3, 2021 - 11:34:09 AM
Long-term archiving on: : Saturday, March 7, 2020 - 2:17:35 PM


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  • HAL Id : hal-02397045, version 1
  • ARXIV : 1912.03146



Lucas Izydorczyk, Nadia Oudjane, Francesco Russo. McKean Feynman-Kac probabilistic representations of non-linear partial differential equations. 2019. ⟨hal-02397045⟩



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