Abstract
We study the behavior of unbounded Gaussian processes. We give necessary and sufficient conditions for the existence of exact upper sequences for unbounded Gaussian sequences with bounded variances.
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Literature cited
Yu. Ch. Kokaev, “Behavior of the oscillation and conditional Gaussian distributions of linear functionals,” J. Sov. Math.,27, No. 5 (1984).
V. A. Rokhlin, “Basic concepts of measure theory,” Mat. Sb.,25(61), No. 1, 107–150 (1949).
V. N. Sudakov, “Geometric problems of the theory of infinite-dimensional distributions,” Tr. Mat. Inst. Akad. Nauk,161 (1976).
V. N. Sudakov and B. S. Tsirel'son, “Extremal properties of half-spaces for spherically invariant maps,” J. Sov. Math.,16, No. 2 (1981).
B. S. Tsirel'son, “A natural modification of a random process and its application to stochastic functional series and Gaussian measures,” J. Sov. Math.,16, No. 2 (1981).
X. Fernique, “Certaines majorations des lois des fonctions aleatoires Gaussiens, applications au comportement des trajectoires,” in: Fourth International Vilnius Conference on Probability Theory and Mathematical Statistics. Abstracts of Reports [in Russian], Vol. 4, Vilnius (1985), pp. 76–78.
R. M. Dudley, “Sample function of the Gaussian processes,” Ann. Prob.,1, No. 1 (1973).
K. Ito and M. Nisio, “On the oscillation functions of Gaussian processes,” Math. Scand.,22, No. 1, 209–223 (1968).
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Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 158, pp. 5–13, 1987.
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Bokvov, S.G. Upper functions and oscillating Gaussian processes. J Math Sci 43, 2745–2751 (1988). https://doi.org/10.1007/BF01129887
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DOI: https://doi.org/10.1007/BF01129887