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.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2019
- DOI:
- 10.48550/arXiv.1912.03146
- arXiv:
- arXiv:1912.03146
- Bibcode:
- 2019arXiv191203146I
- Keywords:
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- Mathematics - Probability