Limit laws for the maxima of stationary chi-processes under random index

摘要

Let {χ_k(t), t ≥ 0} be a stationary χ-process with k degrees of freedom. In this paper, we consider the maxima M_k(T) = max{χ_k(t), {arbitrary}t ∈ [0,T]} with random index Τ_T, where Τ_T/T converges to a non-degenerate distribution or to a positive random variable in probability, and show that the limit distribution of M_k (Τ_T) exists under some additional conditions.