A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
Probability
2022-12-15 v3 Analysis of PDEs
Abstract
We present an algorithm for the numerical solution of nonlinear parabolic partial differential equations. This algorithm extends the classical Feynman-Kac formula to fully nonlinear partial differential equations, by using random trees that carry information on nonlinearities on their branches. It applies to functional, non-polynomial nonlinearities that are not treated by standard branching arguments, and deals with derivative terms of arbitrary orders. A Monte Carlo numerical implementation is provided.
Cite
@article{arxiv.2201.03882,
title = {A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders},
author = {Jiang Yu Nguwi and Guillaume Penent and Nicolas Privault},
journal= {arXiv preprint arXiv:2201.03882},
year = {2022}
}