Lecturer：Prof. Tommi Sottinen, Vaasa University, Finland
Topic：Representing Gaussian Processes via Brownian Motion With Applications to Stochastic Analysis
Time：Nov. 30th 2015, Fri. 16:00-17:00
Add：Math Building—Lecture Hall 145
Synopses: We show that every separable Gaussian process with integrable variance function admits a Fredholm representation with respect to a Brownian motion. We extend the Fredholm representation to a transfer principle and develop stochastic analysis by using it. In particular, we prove an Ito formula that is, as far as we know, the most general Malliavin-type Ito formula for Gaussian processes so far. Finally, we give applications to equivalence in law and series expansions of Gaussian processes.