Monte Carlo solution of Cauchy problem for a nonlinear parabolic equation

In this paper we consider the Monte Carlo solution of the Cauchy problem or a nonlinear parabolic equation Using the fundamental solution of the heat equation. we obtain a nonlinear integral equation with solution the same as the on partial differential equation On the basis of this integral representation. we construct a probabilistic representation of the solution to our original Cauchy problem This representation is based on a branching stochastic process that allows one to directly sample the solution to the lull nonlinear problem Along a trajectory of these branching stochastic processes we build an unbiased estimator for the solution of original Cauchy problem We then provide results of numerical experiments to validate the numerical method and the underlying stochastic representation (C) 2009 IMACS Published by Elsevier B.V. All rights reserved