Some Compound Fractional Poisson Processes

Fuente: arXiv
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Main Authors: Khandakar, M., Kataria, K. K.
Format: Preprint
Published: 2022
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author Khandakar, M.
Kataria, K. K.
author_facet Khandakar, M.
Kataria, K. K.
contents In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized Pólya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes.
format Preprint
id arxiv_https___arxiv_org_abs_2206_04377
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle Some Compound Fractional Poisson Processes
Khandakar, M.
Kataria, K. K.
Probability
60G22, 60G51
In this paper, we introduce and study fractional versions of three compound Poisson processes, namely, the Bell-Touchard process, the Poisson-logarithmic process and the generalized Pólya-Aeppli process. It is shown that these processes are limiting cases of a recently introduced process by Di Crescenzo et al. (2016), namely, the generalized counting process. We obtain the mean, variance, covariance, long-range dependence property etc. for these processes. Also, we obtain several equivalent forms of the one-dimensional distribution of fractional versions of these processes.
title Some Compound Fractional Poisson Processes
topic Probability
60G22, 60G51
url https://arxiv.org/abs/2206.04377