Seminar

Zoom Link

We discuss a priori estimates for the uniform moments of solutions to the parabolic Anderson equation driven by suitable Gaussian noise with parabolic space–time regularity in (-4/3,-1]. Our approach relies on pathwise estimates obtained via regularity structure techniques, which reduce the problem to tail estimates for a more explicit function of the model. Assuming an abstract time-dependence condition, related to shifting the model by elements of the Cameron–Martin space, we use an isoperimetric inequality to derive appropriate tail bounds for this quantity. Finally, we explain how such shifts can be controlled within an analytic framework when the Cameron–Martin space is a tensor product of Besov spaces.