Extremes of locally stationary chi-square processes with trend

TL;DR

This paper derives exact tail asymptotics for the supremum of locally stationary chi-square processes with trends, using a weak Slepian's lemma, and discusses special cases like squared Brownian bridge and Bessel process.

Contribution

It provides new precise tail asymptotics for a class of locally stationary chi-square processes with trends, extending previous results.

Findings

Exact tail asymptotics for supremum of chi-square processes

Application of a weak Slepian's lemma for chi-square processes

Analysis of special cases like squared Brownian bridge and Bessel process

Abstract

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0; 1) of a class of locally stationary chi-square processes with particular admissible trends. An important tool for establishing our results is a weak version of Slepian's lemma for chi-square processes. Some special cases including squared Brownian bridge and Bessel process are discussed.