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October 16, 2025Open Access

Geometrical subordinated Poisson processes and its extensions

Key Points

The study introduces geometric subordinated Poisson processes, significantly extending existing models.
It derives key distributional properties and discusses asymptotic behavior of correlation structures.
Applications in shock modelling demonstrate potential benefits in practical scenarios.
The paper builds upon earlier work by Meoli, incorporating geometric time-changing techniques.

Abstract

In this paper, we study a generalized version of the Poisson-type process by time-changing it with the geometric counting process. Our work generalizes the work done by Meoli (2023) meoli2023some. We defined the geometric subordinated Poisson process (GSPP), the geometric subordinated compound Poisson process (GSCPP) and the geometric subordinated multiplicative Poisson process (GSMPP) by time-changing the subordinated Poisson process, subordinated compound Poisson process and subordinated multiplicative Poisson process with the geometric counting process, respectively. We derived several distributional properties and many special cases from the above-mentioned processes. We calculate the asymptotic behavior of the correlation structure. We have discussed applications of time-changed generalized compound Poisson in shock modelling.

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Cite This Study

Gupta et al. (Wed,) studied this question.

synapsesocial.com/papers/68f0f51d8dd8ea469b1d6e57 https://doi.org/https://doi.org/10.48550/arxiv.2502.18951

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