On the Limit Behavior of a Sequence of Markov Processes Perturbed in a Neighborhood of the Singular Point

  • A. Yu. Pilipenko Ин-т математики НАН Украины, Киев
  • Yu. E. Prikhod’ko

Abstract

We study the limit behavior of a sequence of Markov processes whose distributions outside any neighborhood of a “singular” point are attracted to a certain probability law. In any neighborhood of this point, the limit behavior can be irregular. As an example of application of the general result, we consider a symmetric random walk with unit jumps perturbed in the neighborhood of the origin. The invariance principle is established for the standard time and space scaling. The limit process is a skew Brownian motion.
Published
25.04.2015
How to Cite
PilipenkoA. Y., and Prikhod’koY. E. “On the Limit Behavior of a Sequence of Markov Processes Perturbed in a Neighborhood of the Singular Point”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 4, Apr. 2015, pp. 499-16, http://umj.imath.kiev.ua/index.php/umj/article/view/2000.
Section
Research articles