Geodesic
Random processes generated by independent variables and the strong convergence of functionals
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 122-126

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In the present paper we get sufficient conditions for the strong convergence of distributions of functionals of a sequence of stochastic processes, linearly generated by independent random variables, in the case when the distributions of these processes converge weakly to a Gaussian measure. 
@article{ZNSL_1987_158_a10,
     author = {G. V. Martynova},
     title = {Random processes generated by independent variables and the strong convergence of functionals},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {122--126},
     publisher = {mathdoc},
     volume = {158},
     year = {1987},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a10/}
}
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G. V. Martynova. Random processes generated by independent variables and the strong convergence of functionals. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part X, Tome 158 (1987), pp. 122-126. http://geodesic.mathdoc.fr/item/ZNSL_1987_158_a10/