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Journal Articles Theory of Stochastic Processes Year : 2019

Limit theorem for perturbed random walks

Théorème limite pour une marche aléatoire perturbée

Hoang-Long Ngo
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Marc Peigné


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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Dates and versions

hal-02155058 , version 1 (13-06-2019)
hal-02155058 , version 2 (02-02-2021)
hal-02155058 , version 3 (04-02-2021)


  • HAL Id : hal-02155058 , version 3


Hoang-Long Ngo, Marc Peigné. Limit theorem for perturbed random walks. Theory of Stochastic Processes, 2019. ⟨hal-02155058v3⟩
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