Il Prof. Claudio Macci (Università di Roma Tor Vergata) terrà il seguente seminario mercoledì 9 ottobre alle ore 16.00 presso la sala riunioni del Dipartimento di Matematica dell’Università di Salerno:

*Titolo*: "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 (non fractional) 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≥0, the conditional joint distribution of the components given their sum is multinomial, as happens for the non fractional 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

Cordiali saluti, Barbara Martinucci