Skellam type processes of order K and beyond

Gupta, Heha, Kumar, Arun and Leonenko, Nikolai ORCID: https://orcid.org/0000-0003-1932-4091 2020. Skellam type processes of order K and beyond. Entropy 22 (11) , 1193. 10.3390/e22111193

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Publisher:	MDPI
ISSN:	1099-4300
Date of First Compliant Deposit:	19 October 2020
Date of Acceptance:	19 October 2020
Last Modified:	02 May 2023 12:31
URI:	https://orca.cardiff.ac.uk/id/eprint/135739

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