  We aim to generalize the homogenisation theorem in \cite{Gehringer-Li-tagged}
for a passive tracer interacting with a fractional Gau{\ss}ian noise to also
cover fractional non-Gau{\ss}ian noises. To do so we analyse limit theorems for
normalized functionals of Hermite-Volterra processes, extending the result in
\cite{Diu-Tran} to power series with fast decaying coefficients. We obtain
either convergence to a Wiener process, in the short-range dependent case, or
to a Hermite process, in the long-range dependent case. Furthermore, we prove
convergence in the multivariate case with both, short and long-range dependent
components. Applying this theorem we obtain a homogenisation result for a
slow/fast system driven by such Hermite noises.
