René Schilling: Some martingales for Levy processes

We show the structure of all martingales of the form $f(X_t)- Ef(X_t)$ or $g(X_t)/E g(X_t)$ where $X_t$ is a Levy process. This is connected with Cauchy's functional equation and the Liouville theorem for Levy processes. (Joint work with Franziska Kühn)

Andreas Kyprianou: Asymptotic moments of spatial branching processes

Abstract: We introduce a very general class of non-local branching particle processes and non-local superproesses for which the asymptotic moments can be computed explicitly as a function of time (our results are agnostic to either category of process). The method we use is extremely robust and we are able to provide similar results for the asymptotic moments of occupation functionals as a function of time.