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

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

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 a...

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Bibliographic Details
Main Authors: Nguwi, Jiang Yu, Penent, Guillaume, Privault, Nicolas
Other Authors: School of Physical and Mathematical Sciences
Format: Article
Language:English
Published: 2023
Subjects:
Science::Mathematics
Fully Nonlinear PDEs
Quasilinear PDEs
Online Access:https://hdl.handle.net/10356/168977
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Institution: Nanyang Technological University
Language: English
Description
Summary: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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