I am a probabilist studying stochastic analysis and infinite dimensional analysis. Brownian motion is actually a probability measure on a continuous path space, which is an infinite dimensional Banach space. So, it is no surprise that infinite dimensional spaces often appear in probability theory. Among them, I studied path spaces and loop spaces among them at the beginning of my career. When I was a post-doc, I met rough path theory, which is a new kind of path space analysis. With this theory one can ”de-randomize” stochastic differential equations by considering not just Brownian motion itself, but also its iterated integrals. Since rough path theory seems very promising, I now concentrate on this theory and its ramifications.

Keywords	Stochastic Analysis, Rough Path Theory, Malliavin Calculus, Stochastic Differential Equation
Faculty , Department	Faculty of Mathematics , Department of Mathematical Sciences