Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method

Agarwal, A. and Claisse, J. (2020) Branching diffusion representation of semi-linear elliptic PDEs and estimation using Monte Carlo method. Stochastic Processes and their Applications, 130(8), pp. 5006-5036. (doi: 10.1016/

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We study semi-linear elliptic PDEs with polynomial non-linearity in bounded domains and provide a probabilistic representation of their solution using branching diffusion processes. When the non-linearity involves the unknown function but not its derivatives, we extend previous results in the literature by showing that our probabilistic representation provides a solution to the PDE without assuming its existence. In the general case, we derive a new representation of the solution by using marked branching diffusion processes and automatic differentiation formulas to account for the non-linear gradient term. We consider several examples and estimate their solution by using the Monte Carlo method.

Item Type:Articles
Keywords:Branching diffusion processes, partial differential equation, semi-linear, elliptic, Monte Carlo method, automatic differentiation formula.
Glasgow Author(s) Enlighten ID:Agarwal, Dr Ankush
Authors: Agarwal, A., and Claisse, J.
Subjects:Q Science > QA Mathematics
College/School:College of Social Sciences > Adam Smith Business School > Economics
Journal Name:Stochastic Processes and their Applications
Journal Abbr.:SPA
ISSN (Online):1879-209X
Published Online:28 February 2020
Copyright Holders:Copyright © 2020 Elsevier B.V.
First Published:First published in Stochastic Processes and their Applications 130(8): 5006-5036
Publisher Policy:Reproduced in accordance with the publisher copyright policy

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