Перегляд за Автор "Stamatiieva, V. V."

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    Asymptotic behavior of thinned multi-level point processes in the generalized birthday problem
    (Igor Sikorsky Kyiv Polytechnic Institute, 2025) Stamatiieva, V. V.
    The joint asymptotic behavior in the generalized birthday problem is studied using the apparatus of multi-level point processes. The analysis is based on a Poissonized model. We introduce a method that combines a common normalization function with a thinning operation for different completion levels. We prove the vague convergence of the constructed thinned point process to a limiting Poisson process with independent levels. As an application, the joint limiting distribution for the number of classes reaching lower completion levels by a random time is derived.