********************************************************************* SEMINARI DI PROBABILITA' E STATISTICA MATEMATICA DIPARTIMENTO DI MATEMATICA "G. PEANO" UNIVERSITA' DEGLI STUDI DI TORINO *********************************************************************

Giovedì 11 Febbraio 2016 alle ore 15:00 in Aula C presso il Dipartimento di Matematica "G. Peano" dell'Università degli Studi di Torino, Via Carlo Alberto 10,

Il Dott. BRUNO TOALDO (Dipartimento di Scienze Statistiche, "Sapienza" Università di Roma)

terrà un seminario dal titolo

INTEGRO-DIFFERENTIAL EQUATIONS AND SEMI-MARKOV PROCESSES

Abstract:

A stochastic process X is semi-Markov in the sense of Gihman and Skorohod if the couple (X(t),J(t)), where J(t) is the sojourn time in the current position, is a strict Markov process. The waiting times between the changes of state of the process are in general non exponential r.v.'s. We study the governing equations (Kolmogorov type equations) for semi-Markov processes. These equations are integro-differential equations that become fractional in some particular and interesting cases. For example this is true when the distribution of the waiting times have Mittag-Leffler distribution. Furthermore we present various sufficient conditions to say that a semi-Markov process is a time-changed Markov process. This last case has interesting consequences on the structure of the governing equation.

Tutti gli interessati sono invitati a partecipare.

-- Federico Polito

Department of Mathematics University of Torino Via Carlo Alberto, 10 10123, Torino, Italy Email: federico.polito@unito.it Tel: +39 011 6702937 Web: www.federicopolito.it