Limit theorem for perturbed random walks

Théorème limite pour une marche aléatoire perturbée

Hoang-Long Ngo , Marc Peigné (1)

1 IDP - Institut Denis Poisson

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.

Mots clés: Invariance principle; Reflected Brownian motion; Renewal function; Skew Brownian motion

Domaines: Systèmes dynamiques [math.DS]; Probabilités [math.PR]

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