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Fractional Skellam Process of Order k

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  • K. K. Kataria

    (Indian Institute of Technology Bhilai)

  • M. Khandakar

    (Indian Institute of Technology Bombay)

Abstract

We introduce and study a fractional version of the Skellam process of order k by time-changing it with an independent inverse stable subordinator. We call it the fractional Skellam process of order k (FSPoK). An integral representation for its one-dimensional distributions and their governing system of fractional differential equations are obtained. We derive the probability generating function, mean, variance and covariance of FSPoK which are utilized to establish its long-range dependence property. Later, we consider two time-changed versions of the FSPoK. These are obtained by time-changing the FSPoK by an independent Lévy subordinator and its inverse. Some distributional properties and particular cases are discussed for these time-changed processes.

Suggested Citation

  • K. K. Kataria & M. Khandakar, 2024. "Fractional Skellam Process of Order k," Journal of Theoretical Probability, Springer, vol. 37(2), pages 1333-1356, June.
    • Handle: RePEc:spr:jotpro:v:37:y:2024:i:2:d:10.1007_s10959-024-01314-8
    DOI: 10.1007/s10959-024-01314-8
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    References listed on IDEAS

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    5. A. Kumar & J. Gajda & A. Wyłomańska & R. Połoczański, 2019. "Fractional Brownian Motion Delayed by Tempered and Inverse Tempered Stable Subordinators," Methodology and Computing in Applied Probability, Springer, vol. 21(1), pages 185-202, March.
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