  We introduce a new class of self-similar Gaussian stochastic processes, where
the covariance is defined in terms of a fractional Brownian motion and another
Gaussian process. A special case is the solution in time to the
fractional-colored stochastic heat equation described in Tudor (2013). We prove
that the process can be decomposed into a fractional Brownian motion (with a
different parameter than the one that defines the covariance), and a Gaussian
process first described in Lei and Nualart (2008). The component processes can
be expressed as stochastic integrals with respect to the Brownian sheet. We
then prove a central limit theorem about the Hermite variations of the process.
