The fractional stochastic heat equation on the circle: Time regularity and potential theory

We consider a system of dd linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S1S1. We obtain sharp results on the Hölder continuity in time of the paths of the solution u={u(t,x)}t∈R+,x∈S1u={u(t,x)}t∈R+,x∈S1. We then establish upper and lower bounds on hitting probabilities of uu, in terms of the Hausdorff measure and Newtonian capacity respectively.