Geometrical subordinated Poisson processes and its extensions
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) \cite{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.
Keywords
Cite
@article{arxiv.2502.18951,
title = {Geometrical subordinated Poisson processes and its extensions},
author = {Neha Gupta and Aditya Maheshwari and Dheeraj Goyal},
journal= {arXiv preprint arXiv:2502.18951},
year = {2025}
}
Comments
19 pages, 8 figures