Precise large deviations for dependent subexponential variables

TL;DR

This paper develops precise large deviation estimates for sums of dependent subexponential variables, focusing on regularly varying and lognormal tails, with applications to large sample covariance matrices.

Contribution

It provides new large deviation results for dependent subexponential sequences, extending existing theory to include regularly varying and lognormal tails.

Findings

Derived precise large deviation asymptotics for dependent subexponential variables.

Applied results to limit theory for maxima of large sample covariance matrices.

Extended large deviation principles to dependent sequences with specific tail behaviors.

Abstract

In this paper we study precise large deviations for the partial sums of a stationary sequence with a subexponential marginal distribution. Our main focus is on distributions which either have a regularly varying or a lognormal-type tail. We apply the results to prove limit theory for the maxima of the entries large sample covariance matrices.