  Under certain mild conditions, limit theorems for additive functionals of
some $d$-dimensional self-similar Gaussian processes are obtained. These limit
theorems work for general Gaussian processes including fractional Brownian
motions, sub-fractional Brownian motions and bi-fractional Brownian motions. To
prove these results, we use the method of moments and an enhanced chaining
argument. The Gaussian processes under consideration are required to satisfy
certain strong local nondeterminism property. A tractable sufficient condition
for the strong local nondeterminism property is given and it only relays on the
covariance functions of the Gaussian processes. Moreover, we give a sufficient
condition for the distribution function of a random vector to be determined by
its moments.
