A Fleming-Viat particle representation of Dirichlet Laplacian

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A Fleming-Viat particle representation of Dirichlet Laplacian

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Title: A Fleming-Viat particle representation of Dirichlet Laplacian
Author: Burdzy, Krzysztof; Holyst, Robert; March, Peter
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.
URI: http://hdl.handle.net/1773/2214

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