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 SM ISO690:2012KOLESNIK, Alexander. Weak convergence of the distributions of Markovian random evolutions in two and three dimensions. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, nr. 3(43), pp. 41-52. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 3(43) / 2003 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 41-52 | ||||||
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We consider Markovian random evolutions performed by a particle mov-
ing 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 → ∞, λ → ∞, v2/λ → 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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| Cuvinte-cheie Weak convergence, random evolution, Wiener process, transition law., random motion |
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