Monday Analysis Seminar: Introduction to Rough Path Theory

Date
2017-11-30 16:30 - 2017-11-30 18:00
Place
Faculty of Science Building #3 Room 210
Speaker/Organizer
Yuzuru Inahama (Kyushu University)
 
In this talk I will explain what rough path theory is all about. This is basically a survey talk for non-experts. Simply put, rough path theory is something like "de-randomization of It\^o's stochastic differential equations." Loosely speaking, we first extend the line integral for generalized paths, i.e., rough paths, by using K. T. Chen's theory on iterated integrals of paths as a guide, then we use it to make It\^o's SDEs deterministic. It can be viewed as a generalization of controlled ODEs. With this theory by T. Lyons, which is in a sense an antitehsis to It\^o's theory, we can look at SDEs from a very different angle. It was born approximately 15 years ago, but only a few people studied it at first. In my view it was around 2010 when rough path theory became very active.
(Moreover, two years ago this theory bore two children, which solves very singular stochastic PDEs like KPZ equation or 3-dim dynamic $\Phi^4$ model with ideas from rough path theory.
One of the two got a Fields medal, which makes the future of rough path look more bright.)

Different day of the week.
Monday Analysis Seminar