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


Patrik Albin

Chalmers, Mathematical Sciences, Mathematical Statistics

University of Gothenburg

Enkelejd Hashorva

University of Lausanne

Lanpeng Ji

Haute Ecole Specialisee de Suisse occidentale

University of Lausanne

Chengxiu Ling

Southwest China Normal University

University of Lausanne

ESAIM - Probability and Statistics

1292-8100 (ISSN) 1262-3318 (eISSN)

Vol. 20 349-366

Subject Categories


Probability Theory and Statistics


Basic sciences



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