Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations

Anthony Le Cavil (1, 2) , Nadia Oudjane (3, 2) , Francesco Russo (1)

1 UMA - Unité de Mathématiques Appliquées
2 EDF R&D - EDF R&D
3 FiME Lab - Laboratoire de Finance des Marchés d'Energie

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 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.

Mots clés: Semilinear Partial Differential Equations; Nonlinear Feynman-Kac type functional; Particle systems; Probabilistic representation of PDEs

Domaines: Probabilités [math.PR]

Anthony Le Cavil, Nadia Oudjane, Francesco Russo. Forward Feynman-Kac type representation for semilinear nonconservative Partial Differential Equations. 2016. ⟨hal-01353757v1⟩