On Multiparameter Generalized Counting Process and its Time-Changed Variants
Probability
2025-10-06 v2
Abstract
We introduce and study a multiparameter version of the generalized counting process (GCP), where there is a possibility of finitely many arrivals simultaneously. We call it the multiparameter GCP. In a particular case, it is uniquely represented as a weighted sum of independent multiparameter Poisson processes. For a specific case, we establish a relationship between the multiparameter GCP and the sum of independent GCPs. Some of its time-changed variants are studied where the time-changing components used are the multiparameter stable subordinator and the multiparameter inverse stable subordinator. An integral of the multiparameter GCP is defined, and its asymptotic distribution is obtained.
Cite
@article{arxiv.2503.23070,
title = {On Multiparameter Generalized Counting Process and its Time-Changed Variants},
author = {Manisha Dhillon and Kuldeep Kumar Kataria},
journal= {arXiv preprint arXiv:2503.23070},
year = {2025}
}