On Multiparameter Generalized Counting Process and its Time-Changed Variants

M. Dhillon () and K. K. Kataria ()
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M. Dhillon: Indian Institute of Technology Bhilai
K. K. Kataria: Indian Institute of Technology Bhilai

Journal of Theoretical Probability, 2025, vol. 38, issue 4, 1-23

Abstract: 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.

Keywords: Multiparameter generalized counting process; Additive Lévy process; Multivariate stable subordinator; 60G51; 60G55; 60G60 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10959-025-01451-8

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