Stochastic PDE with the compact support property: new results and old

Título: Stochastic PDE with the compact support property: new results and old

Resumen: This talk is based on a surprising property of heat equations with noise: depending on the noise coefficient, their solutions may have compact support, unlike their deterministic counterparts. I will first discuss some classical theorems of this type when the equation has white Gaussian noise, and then discuss a recent result which proves the compact support property for a class of stochastic heat equations with stable noise. Along the way we will develop some heuristics for why this property holds, sketch some proof techniques, and perhaps see what all this has to do with a class of spatial branching processes called superprocesses.