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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2003, номер 3, страницы 41–52
(Mi basm205)
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Эта публикация цитируется в 4 научных статьях (всего в 4 статьях)
Research articles
Weak convergence of the distributions of Markovian random evolutions in two and three dimensions
A. D. Kolesnik Institute of Mathematics and Computer Science, Chişinău, Moldova
Аннотация:
We consider Markovian random evolutions performed by a particle moving in $R^2$ and $R^3$ with some finite constant speed $v$ randomly changing its directions at Poisson-paced time instants of intensity
$\lambda>0$ uniformly on the $S_2$ and $S_3$-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.
Ключевые слова и фразы:
Weak convergence, random evolution, random motion, Wiener process, transition law.
Поступила в редакцию: 28.03.2003
Образец цитирования:
A. D. Kolesnik, “Weak convergence of the distributions of Markovian random evolutions in two and three dimensions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2003, no. 3, 41–52
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/basm205 https://www.mathnet.ru/rus/basm/y2003/i3/p41
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