Journal of Applied Probability

Correlated fractional counting processes on a finite-time interval

Luisa Beghin, Roberto Garra, and Claudio Macci

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Abstract

We present some correlated fractional counting processes on a finite-time interval. This will be done by considering a slight generalization of the processes in Borges et al. (2012). The main case concerns a class of space-time fractional Poisson processes and, when the correlation parameter is equal to 0, the univariate distributions coincide with those of the space-time fractional Poisson process in Orsingher and Polito (2012). On the one hand, when we consider the time fractional Poisson process, the multivariate finite-dimensional distributions are different from those presented for the renewal process in Politi et al. (2011). We also consider a case concerning a class of fractional negative binomial processes.

Article information

Source
J. Appl. Probab., Volume 52, Number 4 (2015), 1045-1061.

Dates
First available in Project Euclid: 22 December 2015

Permanent link to this document
https://projecteuclid.org/euclid.jap/1450802752

Digital Object Identifier
doi:10.1239/jap/1450802752

Mathematical Reviews number (MathSciNet)
MR3439171

Zentralblatt MATH identifier
1337.60061

Subjects
Primary: 33E12: Mittag-Leffler functions and generalizations 60G22: Fractional processes, including fractional Brownian motion 60G55: Point processes
Secondary: 60E05: Distributions: general theory

Keywords
Poisson process negative binomial process weighted process

Citation

Beghin, Luisa; Garra, Roberto; Macci, Claudio. Correlated fractional counting processes on a finite-time interval. J. Appl. Probab. 52 (2015), no. 4, 1045--1061. doi:10.1239/jap/1450802752. https://projecteuclid.org/euclid.jap/1450802752


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