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Open AccessArticle

Skellam Type Processes of Order k and Beyond

1
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar, Punjab 140001, India
2
Cardiff School of Mathematics, Cardiff University, Senghennydd Road, Cardiff CF24 4AG, UK
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(11), 1193; https://doi.org/10.3390/e22111193
Received: 31 August 2020 / Revised: 17 October 2020 / Accepted: 19 October 2020 / Published: 22 October 2020
(This article belongs to the Special Issue Fractional Calculus and the Future of Science)
In this article, we introduce the Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular, we discuss the space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Skellam process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Lévy measures, governing difference-differential equations of the introduced processes. Our results generalize the Skellam process and running average of Poisson process in several directions. View Full-Text
Keywords: Skellam process; subordination; Lévy measure; Poisson process of order k; running average Skellam process; subordination; Lévy measure; Poisson process of order k; running average
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MDPI and ACS Style

Gupta, N.; Kumar, A.; Leonenko, N. Skellam Type Processes of Order k and Beyond. Entropy 2020, 22, 1193.

AMA Style

Gupta N, Kumar A, Leonenko N. Skellam Type Processes of Order k and Beyond. Entropy. 2020; 22(11):1193.

Chicago/Turabian Style

Gupta, Neha; Kumar, Arun; Leonenko, Nikolai. 2020. "Skellam Type Processes of Order k and Beyond" Entropy 22, no. 11: 1193.

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