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Limit theorems for a class of random outer measures in infinite urn schemes
Berhane Abebe, Mikhail Chebunin, Artyom Kovalevskii
An urn scheme is a probabilistic model in which balls are placed into urns sequentially and independently of each other. All balls share the same probability distribution for hitti…
Asymptotics of joint orderings of compound Poisson fields
Mikhail Chebunin, Artyom Kovalevskii
We are developing a new method for the analysis of queuing systems with heterogeneous in time and space compound (marked) Poisson input flow. The state space of the input flow is e…
Limit theorems for forward and backward processes of numbers of non-empty urns in infinite urn schemes
Mikhail Chebunin, Artyom Kovalevskii
We study the joint asymptotics of forward and backward processes of numbers of non-empty urns in an infinite urn scheme. The probabilities of balls hitting the urns are assumed to…
Functional central limit theorems for occupancies and missing mass process in infinite urn models
Mikhail Chebunin, Sergei Zuyev
We study the infinite urn scheme when the balls are sequentially distributed over an infinite number of urns labelled 1,2,... so that the urn at every draw gets a ball with pro…
On the accuracy of the poissonisation in the infinite occupancy scheme
Mikhail Chebunin
We obtain asymptotic accuracy of the poissonisation in the infinite occupancy scheme. All results are obtained for integer-valued random variables having a regularly varying distri…
Functional central limit theorems for certain statistics in an infinite urn scheme
Mikhail Chebunin, Artyom Kovalevskii
We investigate a specific infinite urn scheme first considered by Karlin (1967). We prove functional central limit theorems for the total number of urns with at least k balls for d…