Bifurcations in the Coupon Collector's Problem for Two Special Discrete Renewal Processes and Related Aspects of the Loss Mass Problem
2022, v.28, Issue 4, 547-576
In this paper we analyze applications of the loss mass problem to statistics of stochastic processes, i.e.\ when phase space consists of all realizations of two special classes of discrete renewal processes. We prove limit theorems for time of full occupation and find ``bifurcation points'' for their limiting distribution. We also prove CLT for missing probability (loss mass), Turing's statistics. All results are based on the Poisson approximation.
Keywords: loss mass problem, Turing's statistics, renewal process, Poisson approximation, coupon collector's problem