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

We consider a system of d linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S 1 . We obtain sharp results on the Hölder continuity in time of the paths of the solution u = { u ( t , x ) } t ∈ R + , x ∈ S 1 . We then establish upper and lower bounds on hitting probabilities of u , in terms of the Hausdorff measure and Newtonian capacity respectively.