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Recent Developments on Fractional Point Processes

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Nonlocal and Fractional Operators

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 26))

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Abstract

In the last two decades, the theoretical advancement of the point processes witnessed an important and deep interconnection with the fractional calculus. It was also found that the stable subordinator plays a vital role in this connection. The survey intends to present recent results on the fractional versions of point processes. We will also discuss generalization attempted by several authors in this direction. Finally, we present some plots and simulations of the well-known fractional Poisson process of Laskin (2003).

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Authors and Affiliations

  1. Operations Management and Quantitative Techniques Area, Indian Institute of Management Indore, Indore, 453556, India

    Aditya Maheshwari & Reetendra Singh

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  1. Aditya Maheshwari
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  2. Reetendra Singh
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Correspondence to Aditya Maheshwari .

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  1. Department of Statistical Sciences, Sapienza University of Rome, Roma, Italy

    Luisa Beghin

  2. Department of Physics and Astronomy (DIFA), Università di Bologna, Bologna, Italy

    Francesco Mainardi

  3. Department of Mathematics, Università di Bari, Bari, Italy

    Roberto Garrappa

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Maheshwari, A., Singh, R. (2021). Recent Developments on Fractional Point Processes. In: Beghin, L., Mainardi, F., Garrappa, R. (eds) Nonlocal and Fractional Operators. SEMA SIMAI Springer Series, vol 26. Springer, Cham. https://doi.org/10.1007/978-3-030-69236-0_11

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