SPDEs with rough noise in space: Holder continuity of the solution

We consider the stochastic wave and heat equations with affine multiplicative Gaussian noise which is white in time and behaves in space like the fractional Brownian motion with index H is an element of (1/4, 1/2). The existence and uniqueness of the solution to these equations has been proved recently by the authors. In the present note we show that these solutions have modifications which are Holder continuous in space of order smaller than H, and Holder continuous in time of order smaller than gamma, where gamma = H for the wave equation and gamma = H/2 for the heat equation. (C) 2016 Elsevier B.V. All rights reserved.