Electronic Communications in Probability

Convergence of point processes associated with coupon collector’s and Dixie cup problems

Andrii Ilienko

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We prove that, in the coupon collector’s problem, the point processes given by the times of $r^{th}$ arrivals for coupons of each type, centered and normalized in a proper way, converge toward a non-homogeneous Poisson point process. This result is then used to derive some generalizations and infinite-dimensional extensions of classical limit theorems on the topic.

Article information

Electron. Commun. Probab., Volume 24 (2019), paper no. 51, 9 pp.

Received: 29 April 2019
Accepted: 21 August 2019
First available in Project Euclid: 12 September 2019

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Zentralblatt MATH identifier

Primary: 60G55: Point processes 60F17: Functional limit theorems; invariance principles

coupon collector’s problem Dixie cup problem point processes Poisson convergence poissonization

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Ilienko, Andrii. Convergence of point processes associated with coupon collector’s and Dixie cup problems. Electron. Commun. Probab. 24 (2019), paper no. 51, 9 pp. doi:10.1214/19-ECP263. https://projecteuclid.org/euclid.ecp/1568253713

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