Extremes and limit theorems for difference of chi-type processes â-

Patrik Albin; Enkelejd Hashorva; Lanpeng Ji; Chengxiu Ling

doi:10.1051/ps/2016018

Extremes and limit theorems for difference of chi-type processes â-

Patrik Albin
, Enkelejd Hashorva
, Lanpeng Ji
, Chengxiu Ling

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

8 Citations (Scopus)

Abstract

Let {_m,k^(k)(t),t≥ 0},κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P supt [0,T[ _m,k^(k)(t) > u →∞, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.

Original language	English
Pages (from-to)	349-366
Number of pages	18
Journal	ESAIM - Probability and Statistics
Volume	20
DOIs	https://doi.org/10.1051/ps/2016018
Publication status	Published - 2016
Externally published	Yes

Keywords

Berman sojourn limit theorem
Berman's condition
Extremes
Gumbel limit theorem
Stationary Gaussian process
Stationary chi-type process

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10.1051/ps/2016018

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title = "Extremes and limit theorems for difference of chi-type processes {\^a}-",

abstract = "Let \{m,k(k)(t),t≥ 0\},κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P supt [0,T[ m,k(k)(t) > u →∞, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.",

keywords = "Berman sojourn limit theorem, Berman's condition, Extremes, Gumbel limit theorem, Stationary Gaussian process, Stationary chi-type process",

author = "Patrik Albin and Enkelejd Hashorva and Lanpeng Ji and Chengxiu Ling",

note = "Publisher Copyright: {\textcopyright} 2016 EDP Sciences, SMAI.",

year = "2016",

doi = "10.1051/ps/2016018",

language = "English",

volume = "20",

pages = "349--366",

journal = "ESAIM - Probability and Statistics",

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TY - JOUR

T1 - Extremes and limit theorems for difference of chi-type processes â-

AU - Albin, Patrik

AU - Hashorva, Enkelejd

AU - Ji, Lanpeng

AU - Ling, Chengxiu

PY - 2016

Y1 - 2016

N2 - Let {m,k(k)(t),t≥ 0},κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P supt [0,T[ m,k(k)(t) > u →∞, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.

AB - Let {m,k(k)(t),t≥ 0},κ > 0 be random processes defined as the differences of two independent stationary chi-type processes with m and k degrees of freedom. In this paper we derive the asymptotics of P supt [0,T[ m,k(k)(t) > u →∞, u→∞ under some assumptions on the covariance structures of the underlying Gaussian processes. Further, we establish a Berman sojourn limit theorem and a Gumbel limit result.

KW - Berman sojourn limit theorem

KW - Berman's condition

KW - Extremes

KW - Gumbel limit theorem

KW - Stationary Gaussian process

KW - Stationary chi-type process

UR - https://www.scopus.com/pages/publications/84990829284

U2 - 10.1051/ps/2016018

DO - 10.1051/ps/2016018

M3 - Article

AN - SCOPUS:84990829284

SN - 1292-8100

VL - 20

SP - 349

EP - 366

JO - ESAIM - Probability and Statistics

JF - ESAIM - Probability and Statistics

ER -

Extremes and limit theorems for difference of chi-type processes â-

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Keywords

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