We study strictly
parabolic stochastic partial differential equations on $\mathbb{R}^d$, d ≥ 1,
driven
by a Gaussian noise white in time and coloured in space. Assuming that the
coefficients
of the differential operator are random, we give sufficient conditions on the
correlation
of the noise ensuring Hölder continuity for the trajectories of the
solution of the equation.
For self-adjoint operators with deterministic coefficients, the mild and weak
formulation
of the equation are related, deriving path properties of the solution to a
parabolic Cauchy
problem in evolution form.