The invariance principle for functions of stationary Gaussian variables

Let $\{Y_j\}$ – the stationary Gaussian sequence.
$$ G(x)\in L^2\biggl(R^1,\frac1{\sqrt{2\pi}}e^{-x^2/2}\,dx\biggl),\quad X_j=G(Y_j). $$
The invariance principle for $\{X_j\}$ is proved. The representation of limiting process as the stochastic integral is obtained too.