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

@inproceedings{Penent2022AFN, title={A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders}, author={Guillaume Penent and Nicolas Privault}, year={2022} }

We present an algorithm for the numerical solution of nonlinear parabolic partial differential equations with arbitrary gradient nonlinearities. This algorithm extends the classical Feynman-Kac formula to fully nonlinear PDEs using random trees that carry information on nonlinearities on their branches. It applies to functional, nonpolynomial nonlinearities that cannot be treated by standard branching arguments and deals with gradients of any orders, avoiding the integrability issues…

## 2 Citations

A deep branching solver for fully nonlinear partial differential equations

- Computer ScienceArXiv
- 2022

Numerical experiments presented show that this algorithm can outperform deep learning approaches based on backward stochastic differential equations or the Galerkin method, and provide solution estimates that are not obtained by those methods in fully nonlinear examples.

Numerical Methods for Backward Stochastic Differential Equations: A Survey

- MathematicsArXiv
- 2021

This paper focuses on the core features of each method: the main assumptions, the numerical algorithm itself, key convergence properties and advantages and disadvantages, in order to provide an exhaustive up-to-date coverage of numerical methods for BSDEs, with insightful summaries of each and useful comparison and categorization.

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