Extremes of locally stationary chi-square processes with trend

Peng Liu and Lanpeng Ji

Stochastic Processes and their Applications, 2017, vol. 127, issue 2, 497-525

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.

Keywords: Tail asymptotics; Chi-square process; Brownian bridge; Bessel process; Fractional Brownian motion; Generalized Kolmogorov–Dvoretsky–Erdős integral test; Pickands constant; Slepian’s lemma (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2016.06.016

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