A Fleming-Viat particle representation of Dirichlet Laplacian

Abstract

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N [goes to infinity] to the first eigenfunction of the Laplacian in D with the same boundary conditions.