Geodesic
Extremes and limit theorems for difference of chi-type processes
Albin, Patrik1 ; Hashorva, Enkelejd2  ; Ji, Lanpeng2, 3 ; Ling, Chengxiu2, 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

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Let { ζ m , k ( κ ) ( 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 { sup t ∈ [ 0 , T ] ζ m , k ( κ ) ( 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.

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

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/}
}
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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

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