Asymptotic behavior of thinned multi-level point processes in the generalized birthday problem
Вантажиться...
Файли
Дата
2025
Автори
Науковий керівник
Назва журналу
Номер ISSN
Назва тому
Видавець
Igor Sikorsky Kyiv Polytechnic Institute
Анотація
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.
Опис
Ключові слова
generalized birthday problem, multi-level point process, Poisson process, Poissonization, thinning, vague convergence, узагальнена задача про днi народження, багаторiвневий точковий процес, пуассонiвський процес, пуассонiзацiя, прорiдження, груба збiжнiсть
Бібліографічний опис
Stamatiieva, 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.