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On the probability of exceeding some curve by \(\varphi\)-subGaussian random process. (English) Zbl 1064.60064

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.

MSC:

60G15 Gaussian processes
60G07 General theory of stochastic processes
60G18 Self-similar stochastic processes
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