Conditions for boundedness of the supremum of a stochastic process from the space \(\text{Sub}_{\varphi}(\Omega)\). (Ukrainian. English summary) Zbl 0956.60026

Vasylyk, O.

Visn., Mat. Mekh., Kyïv. Univ. Im. Tarasa Shevchenka 1998, No. 1, 8-11 (1998).

Let \(\{\xi(t): t \in T \}\) be a sub-Gaussian random process and let the corresponding space \(\text{Sub}_{\varphi}(\Omega)\) of random variables be generated by the Orlicz \(N\)-function \(\varphi(x),x\in R,\) such that for some \(C > 0\) in a neighborhood of zero \(\varphi(x)=Cx^2.\) Estimates for the distribution of supremum of such processes are obtained. This is a generalization of a theorem by A. E. Dmitrovskij [Theory Probab. Math. Stat. 25, 169-180 (1982); translation from Teor. Veroyatn. Mat. Stat. 25, 154-164 (1981; Zbl 0465.60043)].

Reviewer: O.O.Kurchenko (Kyïv)

MSC:

60G07	General theory of stochastic processes
60E15	Inequalities; stochastic orderings

Keywords:

Orlicz space; sub-Gaussian processes; distribution of supremum

Citations:

Zbl 0504.60047; Zbl 0465.60043