  We study the notions of differentiating and non-differentiating sigma-fields
in the general framework of (possibly drifted) Gaussian processes, and
characterize their invariance properties under equivalent changes of
probability measure. As an application, we investigate the class of stochastic
derivatives associated with shifted fractional Brownian motions. We finally
establish conditions for the existence of a jointly measurable version of the
differentiated process, and we outline a general framework for stochastic
embedded equations.
