Some Poisson-Based Processes at Geometric Times

We consider the composition of three different stochastic processes with an independent geometric random time. First, the parent process is assumed to be a homogeneous Poisson process. We aim at providing the probability law of the derived process in terms of the geometric polynomials, the governing...

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Bibliographic Details
Published in:Journal of statistical physics 2023-05, Vol.190 (6), Article 107
Main Author: Meoli, Alessandra
Format: Article
Language:English
Subjects:
Analysis
Laws, regulations and rules
Mathematical and Computational Physics
Physical Chemistry
Physics
Physics and Astronomy
Quantum Physics
Statistical Physics and Dynamical Systems
Stochastic processes
Theoretical
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Summary:We consider the composition of three different stochastic processes with an independent geometric random time. First, the parent process is assumed to be a homogeneous Poisson process. We aim at providing the probability law of the derived process in terms of the geometric polynomials, the governing equations, its representation as a random sum and establishing its main properties. We study stochastic comparisons and the first-crossing-time problem as well. Next, we take as outer processes both an additive and a multiplicative compound Poisson process. We derive the explicit expression of the distribution of the resulting processes and of their moments and then focus on some special cases. Potential applications are also discussed.
ISSN:1572-9613
0022-4715
1572-9613
DOI:10.1007/s10955-023-03117-3