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A Fleming-Viot particle representation of the Dirichlet Laplacian. (English) Zbl 0982.60078
$$N$$ particles move according to independent Brownian motions in an open subset $$D\subset{\mathbb R}^d$$. Whenever a particle hits the boundary of $$D$$, it jumps to the current location of a uniformly selected particle within $$D$$. Equivalently, the first particle is killed and another particle splits into two particles. It is shown that as $$N\to\infty$$, the particle distribution density converges to the normalized heat equation in $$D$$ with Dirichlet boundary conditions and the stationary distributions converge to the first eigenfunction of the Laplacian in $$D$$ with the same boundary conditions. The model is closely related to that studied by the authors and D. Ingerman [J. Phys. A, Math. Gen. 29, No. 11, 2633-2642 (1996; Zbl 0901.60054)] using heuristic and numerical methods.
Reviewer: M.Quine (Sydney)

##### MSC:
 60J65 Brownian motion 60F05 Central limit and other weak theorems
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