Further results for semiregenerative phenomena

A theory of semiregenerative phenomena was developed by the author. The set of points at which such a phenomenon occurs is called a semi regenerative set. There is a correspondence between a semiregenerative set and the range of a Markov subordinator with a unit drift (or a Markov renewal process in the discrete time case). Prabhu, Tang, and Zhu showed that the properties of semiregenerative sets associated with Markov random walks completely characterize the fluctuation behaviour of these processes in the nondegenerate case and also established a Wiener-Hopf factorization based on these sets. These results are surveyed in this paper.