Recurrence relations and upper bounds are obtained for power moments of generalized hitting times for semi-Markov processes. General necessary and sufficient conditions for the existence of these moments are also found. Applications to hitting times for semi-Markov dynamical systems of linear type, semi-Markov random walks, diffusion processes and queuing systems are discussed.
"Recurrence relations for generalized hitting times for semi-Markov processes." Ann. Appl. Probab. 6 (2) 617 - 649, May 1996. https://doi.org/10.1214/aoap/1034968147