A new approach to constructing probability distributions of fractional counting processes

Nick Laskin

Chaos, Solitons & Fractals, 2024, vol. 186, issue C

Abstract: A new approach to the direct construction of probability distribution functions of fractional counting processes without the use of fractional differential and integral operators is presented. The approach is an alternative to currently existing three fundamental methods to introduce and study fractional Poisson process: fractional Kolmogorov–Feller equation, renewal theory with the Mittag-Leffler function as an interarrival time distribution and the inverse stable subordinator method. The resulting probability distributions are well suited for studying various systems and processes that exhibit long-memory behavior. Applications of the developed approach cover topics in enumerative combinatorics and quantum optics.

Keywords: Fractional counting process; Three-parameter generalized Mittag-Leffler function; Waiting time distribution; Bell polynomials; Stirling numbers; Quantum coherent states (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008208

DOI: 10.1016/j.chaos.2024.115268

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