Extremes on different grids and continuous time of stationary processes

Chengxiu Ling; Zuoxiang Peng; Zhongquan Tan

doi:10.1016/j.jmaa.2018.01.008

Extremes on different grids and continuous time of stationary processes

Chengxiu Ling, Zuoxiang Peng, Zhongquan Tan^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

This paper investigates asymptotical distributions of extremes on different grids and continuous time of stationary processes. The findings show that these joint extremes over certain threshold dependent grids are asymptotically completely dependent, dependent and independent respectively for dense, Pickands and sparse grids. Furthermore, an integral representation of the asymptotic function involved in the approximation is obtained.

Original language	English
Pages (from-to)	150-168
Number of pages	19
Journal	Journal of Mathematical Analysis and Applications
Volume	461
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2018.01.008
Publication status	Published - 1 May 2018
Externally published	Yes

Keywords

Extremal index
Extremes
Gumbel limit theorem
Pickands grids
Stationary processes

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10.1016/j.jmaa.2018.01.008

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abstract = "This paper investigates asymptotical distributions of extremes on different grids and continuous time of stationary processes. The findings show that these joint extremes over certain threshold dependent grids are asymptotically completely dependent, dependent and independent respectively for dense, Pickands and sparse grids. Furthermore, an integral representation of the asymptotic function involved in the approximation is obtained.",

keywords = "Extremal index, Extremes, Gumbel limit theorem, Pickands grids, Stationary processes",

author = "Chengxiu Ling and Zuoxiang Peng and Zhongquan Tan",

note = "Publisher Copyright: {\textcopyright} 2018 Elsevier Inc.",

year = "2018",

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AU - Ling, Chengxiu

AU - Peng, Zuoxiang

AU - Tan, Zhongquan

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N2 - This paper investigates asymptotical distributions of extremes on different grids and continuous time of stationary processes. The findings show that these joint extremes over certain threshold dependent grids are asymptotically completely dependent, dependent and independent respectively for dense, Pickands and sparse grids. Furthermore, an integral representation of the asymptotic function involved in the approximation is obtained.

AB - This paper investigates asymptotical distributions of extremes on different grids and continuous time of stationary processes. The findings show that these joint extremes over certain threshold dependent grids are asymptotically completely dependent, dependent and independent respectively for dense, Pickands and sparse grids. Furthermore, an integral representation of the asymptotic function involved in the approximation is obtained.

KW - Extremal index

KW - Extremes

KW - Gumbel limit theorem

KW - Pickands grids

KW - Stationary processes

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DO - 10.1016/j.jmaa.2018.01.008

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SP - 150

EP - 168

JO - Journal of Mathematical Analysis and Applications

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ER -

Extremes on different grids and continuous time of stationary processes

Abstract

Keywords

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