On maxima of chi-processes over threshold dependent grids

Chengxiu Ling; Zhongquan Tan

doi:10.1080/02331888.2015.1083021

On maxima of chi-processes over threshold dependent grids

Chengxiu Ling, Zhongquan Tan^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

In this paper, with motivation from Piterbarg VI [Discrete and continuous time extremes of Gaussian processes. Extremes. 2004;7(2):161–177] and the considerable interest in stationary chi-processes, we derive asymptotic joint distributions of maxima of stationary strongly dependent chi-processes on a continuous time and a uniform grid on the real axis. Our findings extend those for Gaussian cases and give three involved dependence structures via the strongly dependence condition and the sparse, Pickands and dense grids.

Original language	English
Pages (from-to)	579-595
Number of pages	17
Journal	Statistics
Volume	50
Issue number	3
DOIs	https://doi.org/10.1080/02331888.2015.1083021
Publication status	Published - 3 May 2016
Externally published	Yes

Keywords

Pickands constant
Piterbarg max-discretization theorem
discrete time process
normal comparison lemma
stationary chi-processes

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10.1080/02331888.2015.1083021

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AB - In this paper, with motivation from Piterbarg VI [Discrete and continuous time extremes of Gaussian processes. Extremes. 2004;7(2):161–177] and the considerable interest in stationary chi-processes, we derive asymptotic joint distributions of maxima of stationary strongly dependent chi-processes on a continuous time and a uniform grid on the real axis. Our findings extend those for Gaussian cases and give three involved dependence structures via the strongly dependence condition and the sparse, Pickands and dense grids.

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KW - Piterbarg max-discretization theorem

KW - discrete time process

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On maxima of chi-processes over threshold dependent grids

Abstract

Keywords

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