%0 Journal Article %T Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations %+ Unité de Mathématiques Appliquées (UMA) %+ Laboratoire de Finance des Marchés d'Energie (FiME Lab) %+ Optimisation et commande (OC) %A Lecavil, Anthony %A Oudjane, Nadia %A Russo, Francesco %@ 1744-2508 %J Stochastics: An International Journal of Probability and Stochastic Processes %I Taylor & Francis: STM, Behavioural Science and Public Health Titles %V 91 %N 8 %8 2019 %D 2019 %Z 1608.04871 %R 10.1080/17442508.2019.1594809 %K Particle systems %K Semilinear Partial Differential Equations %K Probabilistic representation of PDEs %K Nonlinear Feynman-Kac type functional %Z 60H10; 60H30; 60J60; 65C05; 65C35; 35K58. %Z Mathematics [math]/Probability [math.PR]Journal articles %X We propose a nonlinear forward Feynman-Kac type equation, which represents the solution of a non-conservative semilinear parabolic Partial Differential Equations (PDE). We show in particular existence and uniqueness. The solution of that type of equation can be approached via a weighted particle system. %G English %2 https://ensta-paris.hal.science/hal-01353757v4/document %2 https://ensta-paris.hal.science/hal-01353757v4/file/TheoreticalPaperRevision3October2018.pdf %L hal-01353757 %U https://ensta-paris.hal.science/hal-01353757 %~ ENSTA %~ UNIV-DAUPHINE %~ INSMI %~ UMA_ENSTA %~ PSL %~ UNIV-PARIS-SACLAY %~ ENSTA-SACLAY %~ EDF %~ UNIV-DAUPHINE-PSL