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

We consider a system of d$d$ linear stochastic heat equations driven by an additive infinite-dimensional fractional Brownian noise on the unit circle S¹$S^1$. We obtain sharp results on the Hölder continuity in time of the paths of the solution u=_{{u(t,x)}t∈R+,x∈S1}$u={\left\{u(t,x)\right\}}_{t\in {\mathbb{R}}_{+},x\in S^1}$. We then establish upper and lower bounds on hitting probabilities of u$u$, in terms of the Hausdorff measure and Newtonian capacity respectively.