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Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1292–1300 (Mi semr996)  

Probability theory and mathematical statistics

The principle of invariance in the Strassen form to the partial sum processes of moving averages of finite order

N. S. Arkashovab

a Novosibirsk State Technical University, K. Marx pr., 20, 630073, Novosibirsk, Russia
b Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia

Abstract: 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.

DOI: https://doi.org/10.17377/semi.2018.15.105

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Bibliographic databases:

Document Type: Article
UDC: 519.214
MSC: 60F17
Received November 8, 2017, published October 26, 2018

Citation: N. S. Arkashov, “The principle of invariance in the Strassen form to the partial sum processes of moving averages of finite order”, Sib. Èlektron. Mat. Izv., 15 (2018), 1292–1300

Citation in format AMSBIB
\Bibitem{Ark18}
\by N.~S.~Arkashov
\paper The principle of invariance in the Strassen form to the partial sum processes of moving averages of finite order
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1292--1300
\mathnet{http://mi.mathnet.ru/semr996}
\crossref{https://doi.org/10.17377/semi.2018.15.105}


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