TY - JOUR
AU - A. Yu. Pilipenko
AU - Yu. E. Prikhod’ko
PY - 2015/04/25
Y2 - 2024/04/18
TI - On the Limit Behavior of a Sequence of Markov Processes Perturbed in a Neighborhood of the Singular Point
JF - Ukrains’kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 67
IS - 4
SE - Research articles
DO -
UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2000
AB - 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.
ER -