Extremes and limit theorems for difference of chi-type processes

Albin, Patrik; Hashorva, Enkelejd; Ji, Lanpeng; Ling, Chengxiu

doi:10.1051/ps/2016018

Albin, Patrik ¹ ; Hashorva, Enkelejd ² ; Ji, Lanpeng ^2,³ ; Ling, Chengxiu ^2,⁴

¹ Department of Mathematical Sciences, Chalmers University of Technology, SE-412, 96 Gothenburg, Sweden.
² Department of Actuarial Science, University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland.
³ Institute for Information and Communication Technologies, HEIG-VD, University of Applied Sciences of Western Switzerland, Route de Cheseaux 1, 1401 Yverdon-les-Bains, Switzerland.
⁴ School of Mathematics and Statistics, Southwest University, Beibei District 400715 Chongqing, China.

ESAIM: Probability and Statistics, Tome 20 (2016), pp. 349-366

Voir la notice de l'article provenant de la source Numdam

Résumé

Let ${ζ_{m, k}^{(κ)} (t), t \geq 0}, κ > 0$ 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 $ℙ {{sup}_{t \in [0, T]} ζ_{m, k}^{(κ)} (t) > u}, u \to \infty$ 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.

Zbl

DOI : 10.1051/ps/2016018

Classification : 60G15, 60G70
Keywords: Stationary Gaussian process, stationary chi-type process, extremes, Berman sojourn limit theorem, Gumbel limit theorem, Berman’s condition

Affiliations des auteurs :

Albin, Patrik ¹ ; Hashorva, Enkelejd ² ; Ji, Lanpeng ^{2, 3} ; Ling, Chengxiu ^{2, 4}

¹ Department of Mathematical Sciences, Chalmers University of Technology, SE-412, 96 Gothenburg, Sweden.
² Department of Actuarial Science, University of Lausanne, UNIL-Dorigny 1015 Lausanne, Switzerland.
³ Institute for Information and Communication Technologies, HEIG-VD, University of Applied Sciences of Western Switzerland, Route de Cheseaux 1, 1401 Yverdon-les-Bains, Switzerland.
⁴ School of Mathematics and Statistics, Southwest University, Beibei District 400715 Chongqing, China.

@article{PS_2016__20__349_0,
     author = {Albin, Patrik and Hashorva, Enkelejd and Ji, Lanpeng and Ling, Chengxiu},
     title = {Extremes and limit theorems for difference of chi-type processes},
     journal = {ESAIM: Probability and Statistics},
     pages = {349--366},
     publisher = {EDP-Sciences},
     volume = {20},
     year = {2016},
     doi = {10.1051/ps/2016018},
     zbl = {1356.60042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2016018/}
}

TY  - JOUR
AU  - Albin, Patrik
AU  - Hashorva, Enkelejd
AU  - Ji, Lanpeng
AU  - Ling, Chengxiu
TI  - Extremes and limit theorems for difference of chi-type processes
JO  - ESAIM: Probability and Statistics
PY  - 2016
SP  - 349
EP  - 366
VL  - 20
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/ps/2016018/
DO  - 10.1051/ps/2016018
LA  - en
ID  - PS_2016__20__349_0
ER  -

%0 Journal Article
%A Albin, Patrik
%A Hashorva, Enkelejd
%A Ji, Lanpeng
%A Ling, Chengxiu
%T Extremes and limit theorems for difference of chi-type processes
%J ESAIM: Probability and Statistics
%D 2016
%P 349-366
%V 20
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/ps/2016018/
%R 10.1051/ps/2016018
%G en
%F PS_2016__20__349_0

Albin, Patrik; Hashorva, Enkelejd; Ji, Lanpeng; Ling, Chengxiu. Extremes and limit theorems for difference of chi-type processes. ESAIM: Probability and Statistics, Tome 20 (2016), pp. 349-366. doi: 10.1051/ps/2016018

Cité par Sources :

Parcourir par

Geodesic

Parcourir par