This paper is concerned with robust performance criteria for linear continuous time invariant stochastic systems driven by statistically uncertain random processes. The uncertainty is understood as the deviation of imprecisely known probability distributions of the input disturbance from those of the standard Wiener process. Using a one-parameter family of conformal maps of the unit disk in the complex plane onto the right half-plane for discrete and continuous time transfer functions, the deviation from the nominal Gaussian white-noise model is quantified by the mean anisotropy for the input of a discrete-time counterpart of the original system. The parameter of this conformal correspondence specifies the time scale for filtered versions of the input and output of the system, in terms of which the worst-case root mean square gain is formulated subject to an upper constraint on the mean anisotropy. The resulting two-parameter counterpart of the anisotropy-constrained norm of the system for the continuous time case is amenable to state-space computation using the methods of the anisotropy-based theory of stochastic robust filtering and control, originated by the author in the mid 1990s.