Geodesic
Weak convergence of the distributions of Markovian random evolutions in two and three dimensions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 41-52.

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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 λ>0 uniformly on the S2 and S3-spheres, respectively. We prove that under the Kac condition $$ v\to\infty,\qquad \lambda\to\infty,\qquad\frac{v^2}{\lambda}\to c,\qquad c>0 $$ 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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A. D. Kolesnik. Weak convergence of the distributions of Markovian random evolutions in two and three dimensions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2003), pp. 41-52. https://geodesic-test.mathdoc.fr/item/BASM_2003_3_a3/

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