Maximum likelihood estimator consistency for ballistic random walk in a parametric random environment

TL;DR

This paper develops a maximum likelihood estimator for the parameters of a one-dimensional ballistic random walk in a parametric random environment, proving its consistency and exploring its numerical performance.

Contribution

It introduces a novel maximum likelihood estimation method for environment parameters in ballistic random walks and proves its consistency as the observation horizon extends.

Findings

MLE is consistent as the target site becomes distant

Numerical experiments demonstrate the estimator's effectiveness

The method applies to i.i.d. parametric environments

Abstract

We consider a one dimensional ballistic random walk evolving in an i.i.d. parametric random environment. We provide a maximum likelihood estimation procedure of the environment parameters based on a single observation of the path till the time it reaches a distant site, and prove that this estimator is consistent as the distant site tends to infinity. We also explore the numerical performances of our estimation procedure.