Geodesic
The invariance principle for functions of stationary Gaussian variables
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 32-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
@article{ZNSL_1980_97_a4,
     author = {V. V. Gorodestkii},
     title = {The invariance principle for functions of stationary {Gaussian} variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {32--44},
     year = {1980},
     volume = {97},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/}
}
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V. V. Gorodestkii. The invariance principle for functions of stationary Gaussian variables. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part VI, Tome 97 (1980), pp. 32-44. http://geodesic.mathdoc.fr/item/ZNSL_1980_97_a4/