Extremes and limit theorems for difference of chi-type processes

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.