Forward Feynman-Kac type representation for semilinear non-conservative partial differential equations

Abstract

ABSTRACTWe propose a non-linear forward Feynman-Kac type equation, which represents the solution of a nonconservative 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.