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Convergence of point processes associated with coupon collector’s and Dixie cup problems. (English) Zbl 1422.60082
Summary: We prove that, in the coupon collector’s problem, the point processes given by the times of \(r^{\mathrm{th}}\) 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.

60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
60F17 Functional limit theorems; invariance principles
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