# Some Compound Fractional Poisson Processes

Source: [Some Compound Fractional Poisson Processes](<https://www.sota2.com/research/paper/68fa5c091e209131ce9cdb77>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T17:24:25.895Z

Authors: M. Khandakar, K. K. Kataria

Published: 2022-06-09T09:40:58.000Z

## Abstract

In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized P\\'olya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2206.04377>)

[PDF](<https://arxiv.org/pdf/2206.04377.pdf>)