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. 
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/
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[1] N. S. Arkashov, V. A. Seleznev, “Formation of a relation of nonlocalities in the anomalous diffusion model”, Theoret. and Math. Phys., 193:1 (2017), 1508–1523 | DOI | MR | Zbl

[2] R. Metzler, J. Klafter, “The random walk's guide to anomalous diffusion: A fractional dynamics approach”, Phys. Rep., 339:1 (2000), 1–77 | DOI | MR | Zbl

[3] A. N. Shiryaev, Probability, Springer-Verlag, New York, 1995 | MR | Zbl

[4] A. I. Olemskoi, A. Ya. Flat, “Application of fractals in condensed-matter physics”, Phys. Usp., 36 (1993), 1087–1128 | DOI | MR

[5] R. R. Nigmatullin, “Fractional integral and its physical interpretation”, Theor. Math. Phys., 90:3 (1992), 242–251 | DOI | MR | Zbl

[6] B. Mandelbrot, J. Van Ness, “Fractional Brownian motions, fractional noise and applications”, SIAM Rev., 10 (1968), 422–437 | DOI | MR | Zbl

[7] N. S. Arkashov, I. S. Borisov, A. A. Mogulskii, “Large Deviation Principle for Partial Sum Processes of Moving Averages”, Theory Probab. Appl., 52:2 (2008), 181–208 | DOI | MR | Zbl

[8] W. Feller, An Introduction to Probability Theory and Its Applications, v. II, John Wiley Sons, New York, 1971 | MR | Zbl

[9] T. Konstantopoulos, A. Sakhanenko, “Convergence and convergence rate to fractional Brownian motion for weighted random sums”, Sib. Elektron. Mat. Izv., 1 (2004), 47–63 | MR | Zbl