English

Skellam Type Processes of Order K and Beyond

Probability 2020-12-02 v2

Abstract

In this article, we introduce Skellam process of order k and its running average. We also discuss the time-changed Skellam process of order k. In particular we discuss space-fractional Skellam process and tempered space-fractional Skellam process via time changes in Poisson process by independent stable subordinator and tempered stable subordinator, respectively. We derive the marginal probabilities, Levy measures, governing difference-differential equations of the introduced processes. Our results generalize Skellam process and running average of Poisson process in several directions.

Keywords

Cite

@article{arxiv.2003.09471,
  title  = {Skellam Type Processes of Order K and Beyond},
  author = {Neha Gupta and Arun Kumar and Nikolai Leonenko},
  journal= {arXiv preprint arXiv:2003.09471},
  year   = {2020}
}

Comments

22 pages, 1 figure

R2 v1 2026-06-23T14:21:59.030Z