Strong law of large numbers for random walks in weakly dependent random scenery

TL;DR

This paper proves a strong law of large numbers for random walks in weakly dependent, non-stationary random scenery, extending existing results in the field.

Contribution

It introduces new conditions on weak dependence and non-stationarity to establish the strong law of large numbers for such random walks.

Findings

Established strong law of large numbers under weak dependence.

Extended previous results to non-stationary scenery.

Provided rate conditions for weak dependence.

Abstract

In this brief note, we study the strong law of large numbers for random walks in random scenery. Under the assumptions that the random scenery is non-stationary and satisfies weakly dependent condition with an appropriate rate, we establish strong law of large numbers for random walks in random scenery. Our results extend the known results in the literature.