  We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are
defined as solutions of a family of stochastic Volterra equations with kernel
given by the Riesz derivative kernel, and leading coefficients given by a
sequence of independent Gamma random variables. We construct a new process by
taking the empirical mean of this sequence. In our framework, the processes
involved are not Markovian, hence the analysis of their asymptotic behaviour
requires some ad hoc construction. In our main result, we prove the almost sure
convergence in the space of trajectories of the empirical means to a given
Gaussian process, which we characterize completely.
