Fractional Skellam Process of Order k

K. K. Kataria () and M. Khandakar ()
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K. K. Kataria: Indian Institute of Technology Bhilai
M. Khandakar: Indian Institute of Technology Bombay

Journal of Theoretical Probability, 2024, vol. 37, issue 2, 1333-1356

Abstract: 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.

Keywords: Skellam distribution; Poisson process of order k; Lévy subordinator; Long-range dependence property; 60G22; 60G55 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10959-024-01314-8

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