Recurrence relations for generalized hitting times for semi-Markov processes (Q1814755)

In this lengthy article the author deals with recurrence relations, upper bounds and necessary and sufficient conditions for the existence of finite moments of generalized hitting times for a semi-Markov process \(\{\eta(t),\;t\geq 0\}\) with arbitrary state space \(X\). Generalized hitting times are random functionals defined on trajectories of \(\eta(t)\) and this class of functionals include ordinary hitting times in domains \(D\subseteq X\) and many others. Applications of hitting times for semi-Markov dynamical systems of linear type, semi-Markov random walks, diffusion processes and queueing systems are discussed. A fairly long list of references is included.