Convergence of Coupon Collecting Process via Wormald's Differential Equation Method

Abstract

To approximate the trajectories of a stochastic process by the solution of some differential equation is widely used in the fields of probability, computer science and combinatorics. In this paper, the convergence of coupon collecting processes is studied via the differential equation techniques originally proposed in Wormald(1995) and modified in Warnke(2019). In other words, we give a novel approach to analysis the classical coupon collector's problem and keep track of all coupons in the process of collecting.