Geodesic
Random maps and Kolmogorov widths
Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 78-83.

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In this paper we consider strong random operators. We present the sufficient conditions on a compact set in a Hilbert space under which its image under a Gaussian strong random operator is well-defined and compact. In addition, we investigate the behavior of Kolmogorov widths of some compacts under a Gaussian strong random operator.
Keywords: Gaussian strong random operator, Kolmogorov width, continuity of Gaussian processes. 
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I. A. Korenovska. Random maps and Kolmogorov widths. Teoriâ slučajnyh processov, Tome 20 (2015) no. 1, pp. 78-83. http://geodesic.mathdoc.fr/item/THSP_2015_20_1_a4/

[1] A. V. Skorokhod, Random linear operators, D.Reidel Publishing Company, Dordrecht, Holland, 1983, 198 pp. | MR

[2] A. A. Dorogovtsev, Stochastic analysis and random maps in Hilbert space, VSP, Utrecht, 1994, ii+109 pp. | MR | Zbl

[3] T. E. Harris, “Coalescing and noncoalescing stochastic flows in $\mathbb{R}_1$”, Stochastic Processes and their Applications, 17 (1984), 187–210 | DOI | MR | Zbl

[4] R. Arratia, Coalescing Brownian motions on the line, PhD Thesis, University of Wisconsin, Madison, 1979 | MR

[5] A. A. Dorogovtsev, “Semigroups of finite-dimensional random projections”, Lithuanian Mathematical Journal, 51:3 (2011), 330–341 | DOI | MR | Zbl

[6] R. J. Adler, J. E. Taylor, Random Fields and Geometry, Springer, 2007 | MR | Zbl

[7] N. N. Vahania, V. I. Tarieladze, S. A. Chobanian, Probability distributions in Banach spaces, Nauka, Moscow, 1985 (in Russian) | MR

[8] V. M. Tikhomirov, Some questions in approximation theory, Izdat. Moskov. Univ., Moscow, 1976, 304 pp. (in Russian) | MR

[9] M. Ledoux, M. Talagrand, Probability in Banach Spaces. Isoperimetry and processes, Springer-Verlag, Berlin, 1991 | MR | Zbl

[10] R. S. Ismagilov, “On $n$-dimensional diameters of compacts in a Hilbert space”, Funktional. Anal. i Prilozhen., 2:2 (1968), 32–39 (in Russian) | MR | Zbl