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IMI/Publicaţii/BASM/Ediţii/BASM n.3 (43), 2003/

Weak convergence of the distributions of Marcovian random evolutions in two and three dimensions. (English)

Authors: Kolesnik Alexander

Abstract

We consider Markovian random evolutions performed by a particle moving in R2 and R3 with some finite constant speed v randomly changing its directions at Poisson-paced time instants of intensity lambda > 0 uniformly on the S2 and S3-spheres, respectively. We prove that under the Kac condition v -> infinity, lambda -> infinity , (v2\lambda) -> c, c > 0 the transition laws of the motions weakly converge in an appropriate Banach space to the transition law of the two- and three-dimensional Wiener process, respectively, with explicitly given generators.

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