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Conference Papers Year : 2019

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

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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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Dates and versions

hal-02397045 , version 1 (06-12-2019)

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Lucas Izydorczyk, Nadia Oudjane, Francesco Russo. McKean Feynman-Kac probabilistic representations of non-linear partial differential equations. Geometry and Invariance in Stochastic Dynamics, S. Ugolini et alia, 2019, Verona, Italy. ⟨10.1007/978-3-030-87432-2⟩. ⟨hal-02397045⟩
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