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.
