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