Abstract
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.
Highlights
1 Introduction Poisson processes with randomized time have been intensively studied in the recent literature
The most popular models of such processes are represented by the spacefractional and time-fractional Poisson processes where a random time-change is introduced by a stable subordinator or its inverse correspondingly
In the papers [5, 9] time-changed Poisson processes were studied for the case where the role of time is played by compound Poisson-Gamma subordinators and their inverse processes
Summary
Poisson processes with randomized time have been intensively studied in the recent literature. In the paper [14] a general class of time-changed Poisson processes N f (t) = N (H f (t)), t > 0, has been introduced and studied, where N (t) is a Poisson pro-. Distributional properties, hitting times and governing equations for such processes were presented in [14, 7]; the case of iterated time change and some further generalizations of the class of process N f (t) were considered in [7]. In the papers [5, 9] time-changed Poisson processes were studied for the case where the role of time is played by compound Poisson-Gamma subordinators and their inverse processes.
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