Extremes and limit theorems for difference of chi-type processes
Journal article, 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
Author
Patrik Albin
Chalmers, Mathematical Sciences, Mathematical Statistics
University of Gothenburg
Enkelejd Hashorva
Universitat Lausanne Schweiz
Lanpeng Ji
Haute Ecole Specialisee de Suisse occidentale
Universitat Lausanne Schweiz
Chengxiu Ling
Southwest China Normal University
Universitat Lausanne Schweiz
ESAIM - Probability and Statistics
1292-8100 (ISSN) 1262-3318 (eISSN)
Vol. 20 349-366Subject Categories (SSIF 2011)
Mathematics
Probability Theory and Statistics
Roots
Basic sciences
DOI
10.1051/ps/2016018