Extremes of locally stationary chi-square processes with trend

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.

26 pages in Stochastic Processes and their Applications, 2016

References in corpus (3)

• On the infimum attained by the reflected fractional Brownian motion
• Extremes of a class of nonhomogeneous Gaussian random fields
• Generalized Pickands constants and stationary max-stable processes

Cited by in corpus (5)

• Extremes of Locally-stationary Chi-square processes on discrete grids
• Extremes of locally stationary Gaussian and chi fields on manifolds
• Extremes of Gaussian random fields with non-additive dependence structure
• Tail Asymptotic Behavior of the supremum of a class of chi-square processes
• Extremes of $L^p$-norm of Vector-valued Gaussian processes with Trend