Extremes and limit theorems for difference of chi-type processes
Artikel i vetenskaplig tidskrift, 2016
© 2016 EDP Sciences, SMAI. 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.
Gumbel limit theorem
stationary chi-type process / extremes
Berman sojourn limit theorem
Berman’s condition
Stationary Gaussian process
Författare
Patrik Albin
Chalmers, Matematiska vetenskaper, Matematisk statistik
Göteborgs universitet
Enkelejd Hashorva
Université de Lausanne
Lanpeng Ji
Haute Ecole Specialisee de Suisse occidentale
Université de Lausanne
Chengxiu Ling
Southwest China Normal University
Université de Lausanne
ESAIM - Probability and Statistics
1292-8100 (ISSN) 1262-3318 (eISSN)
Vol. 20 349-366Ämneskategorier
Matematik
Sannolikhetsteori och statistik
Fundament
Grundläggande vetenskaper
DOI
10.1051/ps/2016018