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math.PR2022
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…
math.PR2022
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…
math.PR2016
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…