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.

Correlated fractional counting processes on a finite-time interval / Beghin, Luisa; Garra, Roberto; Macci, Claudio. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 52:4(2015), pp. 1045-1061.

Correlated fractional counting processes on a finite-time interval

BEGHIN, Luisa
;
GARRA, ROBERTO;
2015

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.
2015
negative binomial process; poisson process; weighted process; mathematics (all); statistics and probability; statistics, probability and uncertainty
01 Pubblicazione su rivista::01a Articolo in rivista
Correlated fractional counting processes on a finite-time interval / Beghin, Luisa; Garra, Roberto; Macci, Claudio. - In: JOURNAL OF APPLIED PROBABILITY. - ISSN 0021-9002. - STAMPA. - 52:4(2015), pp. 1045-1061.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/865214
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