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Journal Articles ALEA : Latin American Journal of Probability and Mathematical Statistics Year : 2022

Compound Poisson approximation for simple transient random walks in random sceneries

Abstract

Given a simple transient random walk $(S_n)_{n\geq 0}$ in $\mathbf{Z}$ and a stationary sequence of real random variables $(\xi(s))_{s\in \mathbf{Z}}$, we investigate the extremes of the sequence $(\xi(S_n))_{n\geq 0}$. Under suitable conditions, we make explicit the extremal index and show that the point process of exceedances converges to a compound Poisson point process. We give two examples for which the cluster size distribution can be made explicit.
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Dates and versions

hal-04066232 , version 1 (12-04-2023)

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Nicolas Chenavier, Ahmad Darwiche, Arnaud Rousselle. Compound Poisson approximation for simple transient random walks in random sceneries. ALEA : Latin American Journal of Probability and Mathematical Statistics, 2022, 21 (1), pp.293. ⟨10.30757/ALEA.v21-12⟩. ⟨hal-04066232⟩
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