  This paper considers the class of stochastic processes $X$ which are Volterra
convolutions of a martingale $M$. When $M$ is Brownian motion, $X$ is Gaussian,
and the class includes fractional Brownian motion and other Gaussian processes
with or without homogeneous increments. Let $m$ be an odd integer. Under some
technical conditions on the quadratic variation of $M$, it is shown that the
$m$-power variation exists and is zero when a quantity $\delta^{2}(r) $ related
to the variance of an increment of $M$ over a small interval of length $r$
satisfies $\delta(r) = o(r^{1/(2m)}) $. In the case of a Gaussian process with
homogeneous increments, $\delta$ is $X$'s canonical metric and the condition on
$\delta$ is proved to be necessary, and the zero variation result is extended
to non-integer symmetric powers. In the non-homogeneous Gaussian case, when
$m=3$, the symmetric (generalized Stratonovich) integral is defined, proved to
exist, and its It\^o's formula is proved to hold for all functions of class
$C^{6}$.

Probability