Regularity properties of the solution to a stochastic heat equation driven by a fractional Gaussian noise on [formula omitted

Abstract

We study the linear stochastic heat equation driven by an additive infinite dimensional fractional Brownian noise on the unit sphere S2. The existence and uniqueness of its solution in certain Sobolev space is investigated and sample path regularity properties are established. In particular, the exact uniform modulus of continuity of the solution in time/spatial variable is derived.