On some extensions of generalized counting processes

Lyudmyla Sakhno; Artem Storozhuk

On some extensions of generalized counting processes

Тип публікації :

Препринт

Дата випуску :

1 квітня 2026 р.

Автор(и) :

Lyudmyla Sakhno

Artem Storozhuk

eKNUTSHIR URL :

https://ir.library.knu.ua/handle/15071834/34280

Журнал :

arXiv (Cornell University)

Цитування :

[APA 7] Lyudmyla, S., & Artem, S. (2026). On some extensions of generalized counting processes. arXiv (Cornell University),. https://ir.library.knu.ua/handle/15071834/34280

[ДСТУ] Lyudmyla S., Artem S. On some extensions of generalized counting processes. arXiv (Cornell University). 2026. URL: https://ir.library.knu.ua/handle/15071834/34280 (дата звернення: 11.09.2026).

We study different fractional extensions of the Poisson process and generalized counting processes by introducing time-change represented by the inverse to the sums of stable and tempered stable subordinators. We state the governing equations for probability distributions and probability generating functions which involve fractional derivatives of different orders. Closed form expressions for probability distributions and probability generating functions are also provided for several considered models.

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