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Journal of Theoretical Probability

, Volume 14, Issue 2, pp 485–494 | Cite as

Weak Convergence of a Planar Random Evolution to the Wiener Process

  • Alexander D. Kolesnik
Article

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.

weak convergence random evolution random motions 

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Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • Alexander D. Kolesnik
    • 1
  1. 1.Institute of MathematicsKishinevMoldova

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