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A stochastic simulation for solving scalar reaction–diffusion equations

Published online by Cambridge University Press:  01 July 2016

B. Chauvin  and
Rouault
B. Chauvin*
Affiliation:
Université Paris VI
Rouault*
Affiliation:
Université Paris XI
*
∗Postal address: Université Paris VI, Laboratoire de Probabilités, 4, Place Jussieu, tour 56, 3 ème étage ‐ 75230 Paris Cedex 05, France.
∗∗Postal address: UA-CNRS 743, Statistique Appliquée, Université Paris Sud Mathématiques, Bat. 425, 91405 Orsay Cedex, France.
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Abstract

A recent Monte Carlo method for solving one-dimensional reaction–diffusion equations is considered here as a convergence problem for a sequence of spatial branching processes with interaction. The martingale problem is studied and a limit theorem is proved by embedding spaces of measures in Sobolev spaces.

Keywords

REACTION–DIFFUSION EQUATIONSPATIAL BRANCHING PROCESSESMARTINGALE PROBLEMMONTE CARLO METHODSOBOLEV SPACES
Type
Research Article
Information
Advances in Applied Probability , Volume 22 , Issue 1 , March 1990 , pp. 88 - 100
Copyright
Copyright © Applied Probability Trust 1990 

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