INVESTIGATION OF THE ASYMPTOTICS OF A RENEWAL MATRIX

N. V. BUHRII

Theory of Stochastic Processes Vol. 12 (28), no. 1–2, 2006, pp. 33–37

A semi-Markov process with finite state space and continuous time without finiteness condition of a mean stay time of this process in every fixed state is considered. The asymptotic behaviour of the renewal matrix at infinity is established under condition that the distribution tail of the stay time of the semi-Markov process in every fixed state is a regularly varying function at infinity with exponent -1.

Full version