Geodesic
The principle of invariance in the Donsker form to the partial sum processes of finite order moving averages
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1276-1288

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We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian approximation of this process of partial sums with the aid of a certain class of Gaussian processes, and obtain sufficient conditions for the $C$-convergence in the invariance principle in the Donsker form.
Keywords: invariance principle, fractal Brownian motion, moving average, Gaussian process, memory function, regular varying function. 
@article{SEMR_2019_16_a40,
     author = {N. S. Arkashov},
     title = {The principle of invariance in the {Donsker} form to the partial sum processes of finite order moving averages},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1276--1288},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a40/}
}
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N. S. Arkashov. The principle of invariance in the Donsker form to the partial sum processes of finite order moving averages. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1276-1288. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a40/