Tempered Fractional Poisson Processes and Fractional Equations with Z-Transform

2018/08/02 by Gupta, Neha, Kumar, Arun, Leonenko, Nikolai · 3 citations
#FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.1808.00759

Abstract

In this article, we derive the state probabilities of different type of space- and time-fractional Poisson processes using z-transform. We work on tempered versions of time-fractional Poisson process and space-fractional Poisson processes. We also introduce Gegenbauer type fractional differential equations and their solutions using z-transform. Our results generalize and complement the result available on fractional Poisson processes in several directions.

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• Martingale Characterizations of Non-Homogeneous Counting Processes and Their Fractional Variants
• Time-changed generalized fractional Skellam process
• Tempered Erlang Queue with Multiple Arrivals

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