Kolmogorov equations in infinite dimensions

Abstract: Kolmogorov backward equations related to stochastic evolution equations (SEE) in Hilbert space, driven by trace class Gaussian noise have been intensively studied in the literature. In this talk I discuss the extension to non trace class Gaussian noise in the particular case when the leading linear operator generates an analytic semigroup. This natural generalization leads to several complications, requiring new existence and uniqueness results for SEE with initial singularities and a new notion of an extended transition semigroup. This is joint work with Arnulf Jentzen and Ryan Kurniawan (ETH).