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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Published in:Journal of statistical physics 2023-05, Vol.190 (6), Article 107
Main Author: Meoli, Alessandra
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Language:English
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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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description 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.
doi_str_mv 10.1007/s10955-023-03117-3
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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
title Some Poisson-Based Processes at Geometric Times
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