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<p>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 [<CitationRef CitationID="CR15">15</CitationRef>] 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 [<CitationRef CitationID="CR15">15</CitationRef>] in which the large deviation principle has been established for the empirical measure of Brownian motion.</p>

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A Strong Large Deviation Principle for the Empirical Measure of Random Walks

  • 期刊论文

  • 发表日期：

    2025年6月7日

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  • Dirk Erhard,
  • Tertuliano Franco,
  • Joedson de Jesus Santana

摘要

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 [15] 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 [15] in which the large deviation principle has been established for the empirical measure of Brownian motion.