Limit theorems for additive functionals of random walks in random scenery

2021/01/04 by Françoise Pène, Pene, Françoise
Economics, Econometrics and Finance · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Random Matrices and Applications #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2101.00890

openalex publication_date 2021/01/04 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behaviour of additive functionals of random walks in random scenery. We establish bounds for the moments of the local time of the Kesten and Spitzer process.These bounds combined with a previous moment convergence result (and an ergodicity result) imply the convergence in distribution of additive observables (with a normalization in n^(1/4)).When the sum of the observable is null, the previous limit vanishes and we prove the convergence in the sense of moments (with a normalization in n^(1/8)).

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