The heavy range of randomly biased walks on trees

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:130

Article

Andreoletti, Pierre¹  Diel, Roland² 

[1] Univ Orleans, Inst Denis Poisson, UMR CNRS 7013, Orleans, France

[2] Univ Cote dAzur, LJAD, CNRS, Nice, France

关键词: Randomly biased random walks;    Branching random walks;    Range;    Non-parametric estimation;   

DOI  :  10.1016/j.spa.2019.04.004

来源: Elsevier

【 摘 要 】

We focus on recurrent random walks in random environment (RWRE) on Galton-Watson trees. The range of these walks, that is the number of sites visited at some fixed time, has been studied in three different papers Andreoletti and Chen (2018), Aidekon and de Raphelis (2017) and de Raphelis (2016). Here we study the heavy range: the number of edges frequently visited by the walk. The asymptotic behavior of this process when the number of visits is a power of the number of steps of the walk is given for all recurrent cases. It turns out that this heavy range plays a crucial role in the rate of convergence of an estimator of the environment from a single trajectory of the RWRE. (C) 2019 Elsevier B.V. All rights reserved.

【 授权许可】

Free