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Limit theorem for perturbed random walks

Authors
  • Ngo, Hoang-Long
  • Peigné, Marc
Publication Date
Jun 13, 2019
Source
HAL
Keywords
Language
English
License
Unknown
External links

Abstract

We consider random walks perturbed at zero which behave like (possibly different) random walks with i.i.d. increments on each half lines and restarts at 0 whenever they cross that point. We show that the perturbed random walk, after being rescaled in a proper way, converges to a skew Brownian motion whose parameter is defined by renewal functions of the simple random walks and the transition probabilities from 0.

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