We present some correlated fractional counting processes on a finite-timeinterval. This will be done by considering a slight generalization of theprocesses in Borges et al. (2012). The main case concerns a class ofspace-time fractional Poisson processes and, when the correlation parameter isequal to 0, the univariate distributions coincide with those of the space-timefractional Poisson process in Orsingher and Polito (2012). On the one hand,when we consider the time fractional Poisson process, the multivariatefinite-dimensional distributions are different from those presented for therenewal process in Politi et al. (2011). We also consider a caseconcerning a class of fractional negative binomial processes.
"Correlated fractional counting processes on a finite-time interval." J. Appl. Probab. 52 (4) 1045 - 1061, December 2015. https://doi.org/10.1239/jap/1450802752