Dear all,
this is to announce the following research talk by Claudio Macci, to be held in Pisa.
PLACE: Sala Seminari, Dipartimento di Matematica, Università di Pisa (first floor).
DATE & TIME: Wednesday, Nov 6, 2019, 3 PM
SPEAKER: Claudio Macci (Università Roma Tor Vergata)
TITLE: Multivariate fractional (possibly compound) Poisson processes
ABSTRACT: 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. In particular we show that, for each fixed $t\geq 0$, the conditional joint distribution of the components given their sum is multinomial, as happens for the nonfractional Poisson processes. Thus we consider a suitable multivariate "alternative" fractional Poisson process, and we study its asymptotic behavior for large times (large and moderate deviations). The results appear in two papers with Luisa Beghin.
Best, Dario