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arXiv · 1912.03146

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

Lucas Izydorczyk·Nadia Oudjane·Francesco Russo
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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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Lucas Izydorczyk, Nadia Oudjane, Francesco Russo. 2019-12-06. McKean Feynman-Kac probabilistic representations of non-linear partial differential equations. https://arxiv.org/abs/1912.03146

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