Technical Note—A Limit Theorem on Subintervals of Interrenewal Times

Publisher Website
Google Scholar
Abstract
Consider a renewal process {Xn, n ≥ 1} for which there is defined an associated sequence of independent and identically distributed random variables {Bn, n ≥ 1} such that Bn is the length of a subinterval of Xn. We show that when attention is restricted only to B-intervals, the asymptotic joint distribution of the residual life and total life of a B-interval is that of a renewal process generated by {Bn, n ≥ 1}.