Dipartimento di Matematica, Università di Roma “Tor Vergata” PhD School in Mathematics Announcement of a PhD course (10 hours, online) Paolo Pigato (Università di Roma "Tor Vergata", WIAS Berlin): Fractional Brownian motion and non-Markovian modeling Abstract. In several applications of stochastic analysis (financial engineering, telecommunication networks, ...), it is desirable to model real-world quantities which are non-Markovian, for example because the noise process exhibits slowly decaying auto-correlations and long memory. In this course we will focus on fractional Brownian motion, a prototypical example of non-Markovian process. Such process is a generalisation of Brownian motion with Holder regularity possibly different than 1/2 and it is not a martingale. We will consider large deviations problems, simulation methods and some examples of application. Schedule. - Friday June 05, 2020; h. 14-16 - Tuesday June 09, 2020; h. 14-16 - Thursday June 11, 2020; h. 14-16 - Tuesday June 16, 2020; h. 14-16 - Thursday June 19, 2020; h. 14-16 Information at http://www.mat.uniroma2.it/~dott/corsi.html <http://www.mat.uniroma2.it/~dott/corsi.html> http://www.mat.uniroma2.it/~macci/corso-dottorato-pigato.htm <http://www.mat.uniroma2.it/~macci/corso-dottorato-pigato.htm> How to join the course. The course will take place on the "Teams" platform. Those who do not have an account on Teams can join the course through Chrome or Edge. Please write to caramell@mat.uniroma2.it <mailto:caramell@mat.uniroma2.it> (subject: PhD course) to be part of the mailing list to which instructions for accessing the course will be sent.