Scaling limit theorems for the κ-transient random walk in random and non-random environment

2014/12/14 by Wenming Hong, Hui Yang, Hong, Wenming +1
Decision Sciences · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and statistical mechanics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1412.4326

openalex publication_date 2014/12/14 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

Abstract

Kesten et al.( 1975) proved the stable law for the transient RWRE (here we refer it as the κ-transient RWRE). After that, some similar interesting properties have also been revealed for its continuous counterpart, the diffusion proces in a Brownian environment with drift κ. In the present paper we will investigate the connections between these two kind of models, i.e., we will construct a sequence of the κ-transient RWREs and prove it convergence to the diffusion proces in a Brownian environment with drift κ by proper scaling. To this end, we need a counterpart convergence for the κ-transient random walk in non-random environment, which is interesting itself.

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