×

On the distribution of the supremum of some classes of pre-Gaussian random processes. (English. Russian original) Zbl 0880.60036

Theory Probab. Math. Stat. 49, 103-109 (1994); translation from Teor. Jmovirn. Mat. Stat. 49, 145-154 (1993).
The author considers stochastic processes of the form \(\xi(t)=\sum_{k=1}^{\infty} \xi_k f_k (t)\), \(t\in T\), where \(\{\xi_k\}\) is a sequence of independent centered pre-Gaussian random variables, and \(\{f_k(t)\}\) is a sequence of nonrandom functions. Under some condition on \(\{\xi_k\}\) and \(\{f_k(t)\}\), exponential inequalities are proved for distributions of the random values \(\sup_{t\in T} \xi(t)\) and \(\inf_{t\in T} \xi(t)\).

MSC:

60G15 Gaussian processes
60G17 Sample path properties
PDFBibTeX XMLCite