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

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We study extreme value theory of right stationary Gaussian processes with parameters in open subsets with compact closure of (not necessarily Abelian) locally compact topological groups. Even when specialized to Euclidian space our result extend results on extremes of stationary Gaussian processes and fields in the literature by means of requiring weaker technical conditions as well as by means of the fact that group stationary processes need not be stationary in the usual sense (that is, with respect to addition as group operation).