Renewal sequences with periodic dynamics (Q2894054)

A periodic version of classical discrete-time renewal sequences is considered, where the period \(T\) of the process is fixed and known. Compared with an ordinary renewal process, in the present case, for a renewal occurring at time \(t\), the time until the next renewal is allowed to depend on the season corresponding to time \(t\). The article presents recursions that enable rapid computation of the renewal probabilities. Moreover, limiting aspects of periodic renewal sequences are studied. As an application, an autocorrelated periodic count model having binomial marginal distributions is constructed.