Extremes for transient random walks in random sceneries under weak\n independence conditions

2019/10/10 by Nicolas Chenavier, Chenavier, Nicolas, Ahmad Darwiche +1
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.1910.04651

openalex publication_date 2019/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \ξ(k), k \∈ \ℤ be a stationary sequence of random\nvariables with conditions of type D(u_n) and D'(u_n). Let S_n, n \∈\n\ℕ be a transient random walk in the domain of attraction of a\nstable law. We provide a limit theorem for the maximum of the first n terms\nof the sequence \ξ(S_n), n \∈ \ℕ as n goes to infinity. This\npaper extends a result due to Franke and Saigo who dealt with the case where\nthe sequence \ξ(k), k \∈ \ℤ is i.i.d.\n

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