Forward Feynman-Kac Type Representation for Semilinear Nonconservative Partial Differential Equations

Anthony LE CAVIL, Nadia OUDJANE and Francesco RUSSO

We propose a nonlinear 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 in the first part of the article. The second part is devoted to the construction of a probabilistic particle algorithm and the proof of its convergence. Illustrations of the efficiency of the algorithm are provided by numerical experiments.