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.
In the paper we present the governing equations for marginal distributions of Poisson and Skellam processes time-changed by inverse subordinators. The equations are given in terms of convolution-type derivatives.
In the paper we consider time-changed Poisson processes where the time is expressed by compound Poisson-Gamma subordinators G(N (t)) and derive the expressions for their hitting times. We also study the time-changed Poisson processes where the role of time is played by the processes of the form G(N (t) + at) and by the iteration of such processes.
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