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Monte Carlo Methods and Applications

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Volume 24, Issue 1

Issues

Monte-Carlo algorithms for a forward Feynman–Kac-type representation for semilinear nonconservative partial differential equations

Anthony Le Cavil
  • ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques Appliquées (UMA), 828 Bd. des Maréchaux, 91120 Palaiseau, France
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/ Nadia Oudjane
  • EDF Lab Paris-Saclay and FiME, Laboratoire de Finance des Marchés de l’Energie, 7 Boulevard Gaspard Monge, 91120 Palaiseau, France
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/ Francesco Russo
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  • ENSTA ParisTech, Université Paris-Saclay, Unité de Mathématiques Appliquées (UMA), 828 Bd. des Maréchaux, 91120 Palaiseau, France
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Published Online: 2018-01-26 | DOI: https://doi.org/10.1515/mcma-2018-0005

Abstract

The paper is devoted to the construction of a probabilistic particle algorithm. This is related to a nonlinear forward Feynman–Kac-type equation, which represents the solution of a nonconservative semilinear parabolic partial differential equation (PDE). Illustrations of the efficiency of the algorithm are provided by numerical experiments.

Keywords: Semilinear partial differential equations; nonlinear Feynman–Kac-type functional; particle systems; Euler schemes

MSC 2010: 60H10; 60H30; 60J60; 65C05; 65C35; 68U20; 35K58

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About the article

Received: 2017-09-13

Accepted: 2018-01-05

Published Online: 2018-01-26

Published in Print: 2018-03-01


Funding Source: Deutsche Forschungsgemeinschaft

Award identifier / Grant number: CRC 1283

The financial support for the third-named author was partially provided by the DFG through the CRC 1283, “Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their application”.


Citation Information: Monte Carlo Methods and Applications, Volume 24, Issue 1, Pages 55–70, ISSN (Online) 1569-3961, ISSN (Print) 0929-9629, DOI: https://doi.org/10.1515/mcma-2018-0005.

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