Ukrainian Mathematical Journal

, Volume 67, Issue 4, pp 564–583 | Cite as

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

  • A. Yu. Pilipenko
  • Yu. E. Prikhod’ko

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.


Markov Chain Brownian Motion Random Walk MARKOV Process Weak Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • A. Yu. Pilipenko
    • 1
  • Yu. E. Prikhod’ko
    • 2
  1. 1.Institute of MathematicsUkrainian National Academy of SciencesKyivUkraine
  2. 2.“Kyiv Polytechnic Institute”Ukrainian National Technical UniversityKyivUkraine

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