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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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
id sg-ntu-dr.10356-168977
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spelling sg-ntu-dr.10356-1689772023-06-26T02:27:50Z A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders Nguwi, Jiang Yu Penent, Guillaume Privault, Nicolas School of Physical and Mathematical Sciences Science::Mathematics Fully Nonlinear PDEs Quasilinear PDEs 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. Ministry of Education (MOE) This research is supported by the Ministry of Education, Singapore, under its Tier 2 Grant MOE-T2EP20120-0005. 2023-06-26T02:27:49Z 2023-06-26T02:27:49Z 2023 Journal Article Nguwi, J. Y., Penent, G. & Privault, N. (2023). A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders. Journal of Evolution Equations, 23(1). https://dx.doi.org/10.1007/s00028-023-00873-3 1424-3199 https://hdl.handle.net/10356/168977 10.1007/s00028-023-00873-3 2-s2.0-85149029410 1 23 en MOE-T2EP20120-0005 Journal of Evolution Equations © 2023 The Author(s), under exclusive licence to Springer Nature Switzerland AG. All rights reserved.
institution Nanyang Technological University
building NTU Library
continent Asia
country Singapore
Singapore
content_provider NTU Library
collection DR-NTU
language English
topic Science::Mathematics
Fully Nonlinear PDEs
Quasilinear PDEs
spellingShingle Science::Mathematics
Fully Nonlinear PDEs
Quasilinear PDEs
Nguwi, Jiang Yu
Penent, Guillaume
Privault, Nicolas
A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
description 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.
author2 School of Physical and Mathematical Sciences
author_facet School of Physical and Mathematical Sciences
Nguwi, Jiang Yu
Penent, Guillaume
Privault, Nicolas
format Article
author Nguwi, Jiang Yu
Penent, Guillaume
Privault, Nicolas
author_sort Nguwi, Jiang Yu
title A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
title_short A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
title_full A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
title_fullStr A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
title_full_unstemmed A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
title_sort fully nonlinear feynman-kac formula with derivatives of arbitrary orders
publishDate 2023
url https://hdl.handle.net/10356/168977
_version_ 1772827792651583488

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