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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, No. 4, pp. 499–516, April, 2015.
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Pilipenko, A.Y., Prikhod’ko, Y.E. On the Limit Behavior of a Sequence of Markov Processes Perturbed in a Neighborhood of the Singular Point. Ukr Math J 67, 564–583 (2015). https://doi.org/10.1007/s11253-015-1101-5
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DOI: https://doi.org/10.1007/s11253-015-1101-5