Multivariate Generalized Counting Process via Gamma Subordination
Probability
2026-01-01 v1
Abstract
In this paper, we study a multivariate gamma subordinator whose components are independent gamma processes subject to a random time governed by an independent negative binomial process. We derive the explicit expressions for its joint Laplace-Stieltjes transform, its probability density function and the associated governing differential equations. Also, we study a time-changed variant of the multivariate generalized counting process where the time is changed by an independent multivariate gamma subordinator. For this time-changed process, we obtain the corresponding L\'evy measure and probability mass function. Later, we discuss an application of the time-changed multivariate generalized counting process to a shock model.
Keywords
Cite
@article{arxiv.2512.25030,
title = {Multivariate Generalized Counting Process via Gamma Subordination},
author = {Manisha Dhillon and Kuldeep Kumar Kataria and Shyan Ghosh},
journal= {arXiv preprint arXiv:2512.25030},
year = {2026}
}