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
▼
Show Figures
Figure 1
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
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 StyleGupta, Neha; Kumar, Arun; Leonenko, Nikolai. 2020. "Skellam Type Processes of Order k and Beyond" Entropy 22, no. 11: 1193.
Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.
Search more from Scilit
