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A process of orthogonalization in the Gauss space. (English. Russian original) Zbl 0947.60002

J. Math. Sci., New York 93, No. 3, 447-453 (1999); translation from Zap. Nauchn. Semin. POMI 228, 300-311 (1996).
A group of orthogonal operators is considered which transforms a given family of Gaussian random variables into a family independent of another given Gaussian family. A way to study distributions of suprema for such families is proposed.

MSC:

60B05 Probability measures on topological spaces
60G15 Gaussian processes
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References:

[1] V. N. Sudakov, ”Geometric problems in the theory of infinite-dimensional probability distributions,”Trudy Mat. Inst. Akad. Nauk SSSR, No. 2 (1979). · Zbl 0417.60029
[2] V. N. Sudakov, ”Gaussian measures. A brief survey,”Rend. Ist. Mat. Univ. Trieste,26, supplemento, 289–325 (1994). · Zbl 0858.60006
[3] A. I. Kostrikin and Yu. I. Manin,Linear Algebra and Geometry [in Russian], Nauka, Moscow (1986).
[4] N. Bourbaki,Espaces Vectoriels Topologiques, Hermann, Paris (1953–1955).
[5] P. R. Halmos,Finite-Dimensional Vector Spaces, Van Nostrand, Princeton (1959). · Zbl 0107.01404
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