Compound Poisson Processes with Two-Sided Reflection

  • D. V. Gusak

Abstract

We consider a compound oscillating Poisson process with two-sided reflection. This process is defined by an upper-semicontinuous compound Poisson process ξ(t) and its functionals, namely the first-exit time of ξ(t) from an interval and the first-exit time of ξ(t) across the upper and lower levels. We study the main characteristics of this oscillating process in terms of the potential and resolvent of the process ξ(t) introduced by Korolyuk. For this purpose, we refine the Pecherskii identities and some other results for upper-semicontinuous Poisson processes.
Published
25.12.2002
How to Cite
GusakD. V. “Compound Poisson Processes With Two-Sided Reflection”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 54, no. 12, Dec. 2002, pp. 1616-25, https://umj.imath.kiev.ua/index.php/umj/article/view/4200.
Section
Research articles