A strong large deviation principle for the empirical measure of random walks

TL;DR

This paper establishes a strong large deviation principle for the empirical measure of certain continuous-time random walks within a translation-invariant topology, extending previous results from Brownian motion to random walks.

Contribution

It introduces a strong large deviation principle for empirical measures of continuous-time random walks in a translation-invariant topology, complementing existing Brownian motion results.

Findings

Proves a strong large deviation principle for random walks' empirical measures.

Applies the topology from Mukherjee and Varadhan to random walks.

Extends large deviation results from Brownian motion to random walks.

Abstract

In this article we show that the empirical measure of certain continuous time random walks satisfies a strong large deviation principle with respect to a topology introduced in~\cite{MV2016} by Mukherjee and Varadhan. This topology is natural in models which exhibit an invariance with respect to spatial translations. Our result applies in particular to the case of simple random walk and complements the results obtained in~\cite{MV2016} in which the large deviation principle has been established for the empirical measure of Brownian motion.