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

Kozachenko, Yuriy; Vasylyk, Olga; Yamnenko, Rostislav

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)

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