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

Anthony Le Cavil, Nadia Oudjane and Francesco Russo
submitted
Publication type:
Paper in peer-reviewed journals
arXiv:
images/icons/icon_arxiv.png 1608.04871
Keywords :
Semilinear Partial Differential Equations; Nonlinear Feynman-Kac type functional; Particle systems; Probabilistic representation of PDEs.
Abstract:
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.
BibTeX:
@article{LeC-Oud-Rus-2200,
    author={Anthony Le Cavil and Nadia Oudjane and Francesco Russo },
    title={Forward Feynman-Kac type representation for semilinear 
           nonconservative Partial Differential Equations },
    year={submitted },
    month={8},
}