Geodesic
The principle of invariance in the Strassen form to the partial sum processes of moving averages of finite order
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1292-1300

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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 having the structure of a two-sided moving average. We study the Gaussian approximation of this process of partial sums with the aid of a certain class of Gaussian processes, and obtain estimates of the rate of convergence in the invariance principle in the Strassen form.
Keywords: invariance principle, fractal Brownian motion, moving average, Gaussian process, memory function, regular varying function. 
@article{SEMR_2018_15_a38,
     author = {N. S. Arkashov},
     title = {The principle of invariance in the {Strassen} form to the partial sum processes of moving averages of finite order},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1292--1300},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a38/}
}
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N. S. Arkashov. The principle of invariance in the Strassen form to the partial sum processes of moving averages of finite order. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 1292-1300. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a38/