Reconciling Itô and Stratonovich

Martin Hairer, Imperial College
Fine Hall 214

We all know that SDEs admit two notions of solutions that each come with their own distinct set of symmetries. Stratonovich solutions are equivariant under changes of variables while Itô solutions satisfy Itô's isometry. We also know that these two symmetries are mutually exclusive. Somewhat surprisingly, it turns out that there is a natural class of SPDEs for which there exists a notion of solution that exhibits both of these symmetries simultaneously...