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