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arXiv · 2201.03882

A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders

Jiang Yu Nguwi·Guillaume Penent·Nicolas Privault
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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.

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Jiang Yu Nguwi, Guillaume Penent, Nicolas Privault. 2022-01-11. A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders. https://arxiv.org/abs/2201.03882

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