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Title: A fully nonlinear Feynman-Kac formula with derivatives of arbitrary orders
Authors: Nguwi, Jiang Yu
Penent, Guillaume
Privault, Nicolas
Keywords: Science::Mathematics
Issue Date: 2023
Source: 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).
Project: MOE-T2EP20120-0005 
Journal: Journal of Evolution Equations 
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.
ISSN: 1424-3199
DOI: 10.1007/s00028-023-00873-3
Schools: School of Physical and Mathematical Sciences 
Rights: © 2023 The Author(s), under exclusive licence to Springer Nature Switzerland AG. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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