Modern Stochastics: Theory and Applications (Jun 2017)

Compositions of Poisson and Gamma processes

  • Khrystyna Buchak,
  • Lyudmyla Sakhno

DOI
https://doi.org/10.15559/17-VMSTA79
Journal volume & issue
Vol. 4, no. 2
pp. 161 – 188

Abstract

Read online

In the paper we study the models of time-changed Poisson and Skellam-type processes, where the role of time is played by compound Poisson-Gamma subordinators and their inverse (or first passage time) processes. We obtain explicitly the probability distributions of considered time-changed processes and discuss their properties.

Keywords