On the tail asymptotics of supremum of stationary χ-processes with random trend

Let ?n(t), t ? 0, be a chi-process with n degrees of freedom. We derive the asymptotic exact result for P(sup t? [0,T] (?n(t) + ?(t)) > u), as u ? ?, where ?(t) is a certain random process independent of ?n(t) and T > 0 is a constant.