Moderate Deviations of Hitting Times for Trajectories of Sums of Independent and Identically Distributed Random Variables

2023/11/09 by Yuheng He, He, Yuheng
Decision Sciences · Mathematics · Biochemistry, Genetics and Molecular Biology · #Probability and Risk Models #Stochastic processes and statistical mechanics #DNA and Biological Computing

paper · pdf · doi:10.48550/arxiv.2311.05409

Abstract

In this paper we establish a moderate deviation principle of the hitting times for trajectories of sums of independent and identically distributed random variables. The main idea of proof is to convert the moderate deviations over a small time interval into the moderate deviations at a point, then utilize the moderate deviations for trajectories of sums of independent random variables given by Hu in \citeHu2001 to get the moderate deviations at a point. By the upper bounds of large deviations for trajectories of sums of independent random variables given by Schuette in \cite Schuette1994, we can prove that our convert doesn't influence the rate function of the moderate deviation.

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