Computing the Drift of Random Walks in Dependent Random Environments

TL;DR

This paper introduces new theoretical methods for numerically computing the drift of one-dimensional random walks in dependent random environments, such as k-dependent and moving average environments, addressing a gap in practical evaluation techniques.

Contribution

It develops novel theory and computational methods specifically for calculating the drift in dependent random environments, expanding beyond independent cases.

Findings

New algorithms for drift computation in dependent environments

Application to k-dependent and moving average environments

Enhanced understanding of random walk behavior in complex settings

Abstract

Although the theoretical behavior of one-dimensional random walks in random environments is well understood, the numerical evaluation of various characteristics of such processes has received relatively little attention. This paper develops new theory and methodology for the computation of the drift of the random walk for various dependent random environments, including $k$-dependent and moving average environments.