André Suess: The Martingale-Measure Approach to SPDEs

In this talk we will focus on the martingale-measure approach to stochastic partial differential equations introduced by John B. Walsh in his 1984 Saint Flour lecture notes. The main difference to other approaches such as the "SDEs in Hilbert spaces" approach (see the book of DaPrato and Zabczyk) is that the solutions are random fields in time and space. The talk consists of a thorough introduction to martingale measures as well as stochastic integration with respect to them. Afterwards, depending on time and the previous knowledge of the participants, we will treat more advanced issues related to the random-field solutions derived by the martingale-measure approach, such as p-moments (p>2), path regularity, existence of densities, large deviation principles, Varadhan-Léandre estimates ...