Random Operators and Stochastic Equations
Editor-in-Chief: Girko, Vyacheslav
Managing Editor: Molchanov, S.
Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre
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CiteScore 2016: 0.37
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Source Normalized Impact per Paper (SNIP) 2016: 0.793
Mathematical Citation Quotient (MCQ) 2016: 0.09
On distribution of the norm of deviation of a sub-Gaussian random process in Orlicz spaces
The paper is devoted to the study of sub-Gaussian random variables and stochastic processes. Recall that along with centered Gaussian random variables the space Sub(Ω) of sub-Gaussian random variables contains all bounded zero-mean random variables and all zero-mean random variables whose distribution tails decrease no slower than the tails of the distribution of a Gaussian random variable. Here we study a square deviation of a sub-Gaussian random process from a constant and derive an upper estimate for the exponential moment of the deviation. The obtained result allows to estimate the distribution of deviation of a sub-Gaussian random process from some measurable function in the norm of Lp(𝕋) and in the norm of Orlicz space. The paper generalizes results of [Theory Probab. Math. Statist. 58 (1999), 51–66] for the norm of a sub-Gaussian random process in Orlicz space. As an example we apply the obtained estimates to a sub-Gaussian Wiener process deviated from a linear and a square root functions.