  We investigate the quality of space approximation of a class of stochastic
integral equations of convolution type with Gaussian noise. Such equations
arise, for example, when considering mild solutions of stochastic fractional
order partial differential equations but also when considering mild solutions
of classical stochastic partial differential equations. The key requirement for
the equations is a smoothing property of the deterministic evolution operator
which is typical in parabolic type problems. We show that if one has access to
nonsmooth data estimates for the deterministic error operator together with its
derivative of a space discretization procedure, then one obtains error
estimates in pathwise H\"older norms with rates that can be read off the
deterministic error rates. We illustrate the main result by considering a class
of stochastic fractional order partial differential equations and space
approximations performed by spectral Galerkin methods and finite elements. We
also improve an existing result on the stochastic heat equation.
