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A new approach to constructing probability distributions of fractional counting processes

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  • Laskin, Nick

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.

Suggested Citation

  • Laskin, Nick, 2024. "A new approach to constructing probability distributions of fractional counting processes," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    • Handle: RePEc:eee:chsofr:v:186:y:2024:i:c:s0960077924008208
    DOI: 10.1016/j.chaos.2024.115268
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