Fractional counting process at Lévy times and its applications Article Swipe

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Sakshi Garg , Ashok Kumar Pathak , Aditya Maheshwari ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2412.04334

Traditionally, fractional counting processes, such as the fractional Poisson process, etc. have been defined using fractional differential and integral operators. Recently, Laskin (2024) introduced a generalized fractional counting process (FCP) by changing the probability mass function (pmf) of the time fractional Poisson process using the generalized three-parameter Mittag-Leffler function. Here, we study some additional properties for the FCP and introduce a time-changed fractional counting process (TCFCP), defined by time-changing the FCP with an independent Lévy subordinator. We derive distributional properties such as the Laplace transform, probability generating function, the moments generating function, mean, and variance for the TCFCP. Some results related to waiting time distribution and the first passage time distribution are also discussed. We define the multiplicative and additive compound variants for the FCP and the TCFCP and examine their distributional characteristics with some typical examples. We explore some interesting connections of the TCFCP with Bell polynomials by introducing subordinated generalized fractional Bell polynomials. It is shown that the moments of the TCFCP can be represented in terms of the subordinated generalized fractional Bell polynomials. Finally, we present the application of the FCP in a shock deterioration model.

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Process (computing) Computer science Counting process Mathematics Statistics Programming language

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2412.04334
PDF: https://arxiv.org/pdf/2412.04334
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Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2412.04334

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Title: Fractional counting process at Lévy times and its applications

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Language: en

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Publication year: 2024

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Publication date: 2024-12-05

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Authors: Sakshi Garg, Ashok Kumar Pathak, Aditya Maheshwari

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Landing page: https://arxiv.org/abs/2412.04334

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Concepts: Process (computing), Computer science, Counting process, Mathematics, Statistics, Programming language

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