Infinite-dimensional aspects of one-dimensional stochastic flows

The aim of this lectures is to introduce the stochastic calculus for the flows of interacting Brownian particles on the real line. Such families of Brownian motions lose some Gaussian features and obtain new. So, the establishing of such results as Girsanov type theorem, Large Deviations Principle, chaotic expansion, Clark representation, requires some new techniques and arguments. In the lectures we will present such new tools. In particular the time of free motion in the continuum particle system and quadratic entropy for such systems will be introduced. Using these new notions we obtain the above mentioned Gaussian style results and some essentially infinite-dimensional properties of the Brownian stochastic flows on the real line as well.

There are 4 lectures per 50 min.