Further results for semiregenerative phenomena (Q1323528)

A theory of semiregenerative phenomena was developed earlier by the author [A celebration of applied probability, J. Appl. Probab., Spec. Vol. 25A, 257-274 (1988; Zbl 0664.60115)]. This phenomenon is a generalization of Feller's recurrent event in discrete time and Kingman's regenerative phenomenon in continuous time. A survey of the results obtained by the author and his collaborators is presented. These include the connection between a semiregenerative set (the points at which the semiregenerative phenomenon occurs) and the range of a Markov subordinator with a unit drift, the fluctuation behaviour of nondegenerate Markov random walk (MRW) and a Wiener-Hopf factorization of the MRW [see the author, \textit{L. C. Tang} and \textit{Y. Zhu}, J. Math. Phys. Sci. 25, No. 5/6, 635-663 (1991; Zbl 0790.60059)].