  Consider estimation of the regression function based on a model with
equidistant design and measurement errors generated from a fractional Gaussian
noise process. In previous literature, this model has been heuristically linked
to an experiment, where the anti-derivative of the regression function is
continuously observed under additive perturbation by a fractional Brownian
motion. Based on a reformulation of the problem using reproducing kernel
Hilbert spaces, we derive abstract approximation conditions on function spaces
under which asymptotic equivalence between these models can be established and
show that the conditions are satisfied for certain Sobolev balls exceeding some
minimal smoothness. Furthermore, we construct a sequence space representation
and provide necessary conditions for asymptotic equivalence to hold.
