Sampling at subexponential times, with queueing applications (Q1593601)

The paper studies the tail asymptotic of the r.v. \(X(T)\), where \((X(t),t\geq 0)\) is a random process with a linear trend satisfying some regularity conditions, e.g. Markov process, and \(T\) is an independent r.v. The results depend on the tail distribution of the r.v. \(T\). Actually, the cases of light-tailed, moderately heavy-tailed and heavy-tailed distributions are considered.