Multivariate fractional Poisson processes and compound sums. (English) Zbl 1351.60045

Beghin, Luisa; Macci, Claudio

Adv. Appl. Probab. 48, No. 3, 691-711 (2016).

Summary: In this paper we present multivariate space-time fractional Poisson processes by considering common random time-changes of a (finite-dimensional) vector of independent classical (nonfractional) Poisson processes. In some cases we also consider compound processes. We obtain some equations in terms of some suitable fractional derivatives and fractional difference operators, which provides the extension of known equations for the univariate processes.

MSC:

60G22	Fractional processes, including fractional Brownian motion
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)
60G52	Stable stochastic processes
34A08	Fractional ordinary differential equations
33E12	Mittag-Leffler functions and generalizations

Keywords:

fractional Poisson processes; conditional independence; Fox-Wright function; fractional differential equation; random time-change