报告人：芬兰Vaasa大学Tommi Sottinen 教授
报告题目：Representing Gaussian processes via Brownian motion with applications to stochastic analysis
摘要：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.