  We consider a stochastic process $Y$ defined by an integral in quadratic mean
of a deterministic function $f$ with respect to a Gaussian process $X$, which
need not have stationary increments. For a class of Gaussian processes $X$, it
is proved that sums of properly weighted powers of increments of $Y$ over a
sequence of partitions of a time interval converge almost surely. The
conditions of this result are expressed in terms of the $p$-variation of the
covariance function of $X$. In particular, the result holds when $X$ is a
fractional Brownian motion, a subfractional Brownian motion and a bifractional
Brownian motion.
