Fractional non-homogeneous counting process

2023/12/28 by Nick Laskin, Laskin, Nick
Mathematics · Physics and Astronomy · #26A33 #33E12 #37A50 #Advanced Statistical Methods and Models #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Distribution Estimation and Applications #Statistical Mechanics and Entropy

paper · pdf · doi:10.48550/arxiv.2312.17389

openalex publication_date 2023/12/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A new fractional non-homogeneous counting process has been introduced and developed using the Kilbas and Saigo three-parameter generalization of the Mittag-Leffler function. The probability distribution function of this process reproduces for certain set of the fractality parameters the famous Poisson and fractional Poisson probability distributions as well as the probability distribution function of a counting process displaying stretched exponential interarrival times distribution. Applications of the developed fractional non-homogeneous counting process cover fractional compound process, the generalization of combinatorial polynomials and numbers, statistics of the fractional non-homogeneous counting process and a new representation of the Kilbas and Saigo function.

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