%0 Unpublished work
%T McKean Feynman-Kac probabilistic representations of non-linear partial differential equations
%+ Unité de Mathématiques Appliquées (UMA)
%+ EDF R&D (EDF R&D)
%+ Optimisation et commande (OC)
%A Izydorczyk, Lucas
%A Oudjane, Nadia
%A Russo, Francesco
%Z The work was supported by a public grant as part of the "Investissement d'avenir project, reference ANR-11-LABX-0056-LMH, LabEx LMH," in a joint call with Gaspard Monge Program for optimization, operations research and their interactions with data sciences.
%8 2019-12-06
%D 2019
%Z 1912.03146
%K Backward diffusion
%K McKean stochastic differential equation
%K Probabilistic representation of PDEs
%K Time reversed diffusion
%K HJB equation
%K Feynman-Kac measures
%Z 60H10; 60H30; 60J60; 65C05; 65C35; 35K58.
%Z Mathematics [math]/Probability [math.PR]Preprints, Working Papers, ...
%X 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.
%G English
%2 https://hal.archives-ouvertes.fr/hal-02397045/document
%2 https://hal.archives-ouvertes.fr/hal-02397045/file/ProcAlbeverioDecember6_2019Sent.pdf
%L hal-02397045
%U https://hal.archives-ouvertes.fr/hal-02397045
%~ INSMI
%~ UMA_ENSTA
%~ EDF
%~ IP_PARIS
%~ ENSTA
%~ IP_PARIS_COPIE