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Weak Convergence of a Planar Random Evolution to the Wiener Process

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  • Alexander D. Kolesnik

    (Institute of Mathematics)

Abstract

The weak convergence of the distributions of a symmetrical random evolution in a plane controlled by a continuous-time homogeneous Markov chain with n, n≥3, states to the distribution of a two-dimensional Brownian motion, as the intensity of transitions tends to infinity, is proved.

Suggested Citation

  • Alexander D. Kolesnik, 2001. "Weak Convergence of a Planar Random Evolution to the Wiener Process," Journal of Theoretical Probability, Springer, vol. 14(2), pages 485-494, April.
    • Handle: RePEc:spr:jotpro:v:14:y:2001:i:2:d:10.1023_a:1011167815206
    DOI: 10.1023/A:1011167815206
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    References listed on IDEAS

    as
    1. Kolesnik, Alexander D. & Turbin, Anatoly F., 1998. "The equation of symmetric Markovian random evolution in a plane," Stochastic Processes and their Applications, Elsevier, vol. 75(1), pages 67-87, June.
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