National Seminar on Probability and Statistics

The next meeting of the National Seminar on Probability and Statistics will be held on June 28, 2017 (Wednesday), at 3:15 p.m. in Room 403 of IMI - BAS.

Bruno Toaldo (Università degli Studi di Napoli Federico II, Napoli, Italy)

will deliver a lecture on:

On semi-Markov processes and their Kolmogorov's equations

Everybody is invited.

Abstract: A process X(t), t > 0, is said to be a semi-Markov process in the sense of Gihman and Skorohod if the couple (X(t), y(t)), where y(t) is the sojourn time in the current position, is a strong (homogeneous) Markov process. We discuss the Kolmogorov's equations of such processes. An evolutionary form (integro-differential) for such equations is presented and related with the construction of semi-Markov processes as time-changed Markov processes. The time-fractional equation is an interesting particular case, obtained when the waiting times between the jumps are i.i.d. r.v.'s with Mittag-Leffler distribution.