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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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https://hal.archives-ouvertes.fr/hal-02155058
Contributor : Marc Peigné <>
Submitted on : Thursday, February 4, 2021 - 11:45:09 AM
Last modification on : Tuesday, February 9, 2021 - 3:18:05 AM

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  • HAL Id : hal-02155058, version 3

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Hoang-Long Ngo, Marc Peigné. Limit theorem for perturbed random walks. 2021. ⟨hal-02155058v3⟩

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