Sib. Èlektron. Mat. Izv., 2018, Volume 15, Pages 1292–1300
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
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.
invariance principle, fractal Brownian motion, moving average, Gaussian process, memory function, regular varying function.
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Received November 8, 2017, published October 26, 2018
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
\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.
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