Electronic Communications in Probability

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

Andrii Ilienko

Full-text: Open access

Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1568253713

Digital Object Identifier
doi:10.1214/19-ECP263

Mathematical Reviews number (MathSciNet)
MR4003125

Zentralblatt MATH identifier
1422.60082

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

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

Rights
Creative Commons Attribution 4.0 International License.

Citation

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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