Hao Tang, University of Oslo
In this talk, I will discuss SPDEs with pseudo-differential noise (non-local in the spatial variable) and mean-field noise (non-local in the sample variable), respectively. In the case of pseudo-differential noise, we discovered certain cancellation properties inherent to pseudo-differential operators, which play key roles in proving the existence of solutions. When it comes to mean-field noise, different from classical SDE/SPDE, relying solely on stopping times techniques does not ensure uniqueness. We have pinpointed a new localized topology that allows us to prove uniqueness even in non-Lipschitz cases. Moreover, we’ve established abstract frameworks for each scenario.