Limit theorem for perturbed random walks

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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Contributor : Marc Peigné <>
Submitted on : Thursday, June 13, 2019 - 12:28:50 PM
Last modification on : Saturday, June 15, 2019 - 1:33:54 AM

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Hoang-Long Ngo, Marc Peigné. Limit theorem for perturbed random walks. 2019. ⟨hal-02155058⟩

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