Stamatiieva, V. V.2026-02-122026-02-122025Stamatiieva, V. V. Asymptotic behavior of thinned multi-level point processes in the generalized birthday problem / V. V. Stamatiieva // Mathematics in Modern Technical University. – 2025. – Vol. 2025, No 2. – P. 55-63. – Bibliog.: 7 ref.https://ela.kpi.ua/handle/123456789/78782The 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.engeneralized birthday problemmulti-level point processPoisson processPoissonizationthinningvague convergenceузагальнена задача про днi народженнябагаторiвневий точковий процеспуассонiвський процеспуассонiзацiяпрорiдженнягруба збiжнiстьArticleP. 55-63https://doi.org/10.20535/mmtu-2025.2-055519.210000-0003-2721-8985