Geodesic
Local asymptotically normality of the Gaussian family of distribution
Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 13-26

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The Gaussian stationary process $X$ with spectral density $f(\theta, \lambda)$ is considered. We shaw that under the suitable conditions on function $f$ the family of Gaussian distribution are satisfied to the condition of the local asymptotically normality. 
@article{ZNSL_1984_136_a1,
     author = {M. S. Ginovyan},
     title = {Local asymptotically normality of the {Gaussian} family of distribution},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--26},
     publisher = {mathdoc},
     volume = {136},
     year = {1984},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a1/}
}
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M. S. Ginovyan. Local asymptotically normality of the Gaussian family of distribution. Zapiski Nauchnykh Seminarov POMI, Studies in mathematical statistics. Part VI, Tome 136 (1984), pp. 13-26. http://geodesic.mathdoc.fr/item/ZNSL_1984_136_a1/