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Асимптотична поведiнка прорiджених багаторiвневих точкових процесiв в узагальненiй задачi про днi народження

Year: 2025

Type: article

Abstract: 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.

Source: The Scientific Issues of Ternopil Volodymyr Hnatiuk National Pedagogical University Series pedagogy

Author: Стаматієва, В. В.

Institution: National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”

Language: English

Topic: Point processes and geometric inequalities

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7117954083

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