Kozachenko, Yuriy; Vasylyk, Olga; Yamnenko, Rostislav On the probability of exceeding some curve by \(\varphi\)-subGaussian random process. (English) Zbl 1064.60064 Theory Stoch. Process. 9(25), No. 3-4, 70-80 (2003). The authors deal with the probability of exceeding some curve by \(\varphi\)-sub-Gaussian random process. Definitions and some properties of \(\varphi\)-sub-Gaussian and strictly \(\varphi\)-sub-Gaussian spaces of random variables and processes are given. General results on estimates of probability that the \(\varphi\)-sub-Gaussian random process overcrosses some level are obtained. The authors estimate the upper bound of probability that the process of strictly \(\varphi\)-sub-Gaussian fractional Brownian motion defined on the interval \([a,b]\) exceeds the function \(f\cdot t,\) where \(f>0\) is a constant. Reviewer: A. D. Borisenko (Kyïv) Cited in 1 ReviewCited in 1 Document MSC: 60G15 Gaussian processes 60G07 General theory of stochastic processes 60G18 Self-similar stochastic processes Keywords:\(\varphi\)-sub-Gaussian stochastic process; fractional Brownian motion; metric entropy PDF BibTeX XML Cite \textit{Y. Kozachenko} et al., Theory Stoch. Process. 9(25), No. 3--4, 70--80 (2003; Zbl 1064.60064) OpenURL