  This paper provides estimates for the convergence rate of the total variation
distance in the framework of the Breuer-Major theorem, assuming some smoothness
properties of the underlying function. The results are proved by applying new
bounds for the total variation distance between a random variable expressed as
a divergence and a standard Gaussian random variable, which are derived by a
combination of techniques of Malliavin calculus and Stein's method. The
representation of a functional of a Gaussian sequence as a divergence is
established by introducing a shift operator on the expansion in Hermite
polynomials. Some applications to the asymptotic behavior of power variations
of the fractional Brownian motions and to the estimation of the Hurst parameter
using power variations are presented.
