Compositions of Poisson and Gamma processes

Khrystyna Buchak, Lyudmyla Sakhno


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.


Time-change; Poisson process; Skellam process; compound Poisson-Gamma subordinator; inverse subordinator

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