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On Distributions of Certain State-Dependent Fractional Point Processes

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  • K. K. Kataria

    (Indian Institute of Technology Bombay)

  • P. Vellaisamy

    (Indian Institute of Technology Bombay)

Abstract

We obtain the explicit expressions for the state probabilities of various state-dependent versions of fractional point processes. The inversion of the Laplace transforms of the state probabilities of such processes is rather cumbersome and involved. We employ the Adomian decomposition method to solve the difference-differential equations governing the state probabilities of these state-dependent processes. The distributions of some convolutions of the Mittag-Leffler random variables are derived as special cases of the obtained results.

Suggested Citation

  • K. K. Kataria & P. Vellaisamy, 2019. "On Distributions of Certain State-Dependent Fractional Point Processes," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1554-1580, September.
    • Handle: RePEc:spr:jotpro:v:32:y:2019:i:3:d:10.1007_s10959-018-0835-z
    DOI: 10.1007/s10959-018-0835-z
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    References listed on IDEAS

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    1. Orsingher, Enzo & Polito, Federico, 2012. "The space-fractional Poisson process," Statistics & Probability Letters, Elsevier, vol. 82(4), pages 852-858.
    2. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    3. Kataria, K.K. & Vellaisamy, P., 2017. "Saigo space–time fractional Poisson process via Adomian decomposition method," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 69-80.
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