Invariance Principles for the Coupon Collector's Problem: A Martingale Approach

Abstract

For the coupon collector's problem, invariance principles for the partial sequence of bonus sums after $n$ coupons as well as the waiting times to obtain the bonus sum $t(\geqslant 0)$ are studied through a construction of a triangular array of martingales related to these sequences and verifying the invariance principles for these martingales.