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On a limit behaviour of a one-dimensional random walk with non-integrable impurity. (English) Zbl 1363.60098
Summary: We consider the limit behaviour of a one-dimensional symmetric random walk that is perturbed at zero. For the natural scaling of time and space the invariance principle is proved. The limit process is a skew Brownian motion.
MSC:
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60F17 Functional limit theorems; invariance principles
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Full Text: MNR