On the rate of convergence in the Lévy-Baxter theorems for certain classes of random processes. (English. Russian original) Zbl 0836.60042

Vovk, L. B.; Kozachenko, Yu. V.

Theory Probab. Math. Stat. 46, 23-32 (1993); translation from Teor. Jmovirn. Mat. Stat. 46, 25-36 (1992).

Summary: The new class of super-Gaussian random variables is introduced. In contrast to sub-Gaussian variables, these are not dominated by Gaussian ones, but dominate them. Super-Gaussian vectors and processes are also considered. Their properties are studied. For random vectors and processes which are simultaneously sub- and super-Gaussian, the conditions and rate of convergence of Baxter sums are considered in the Orlicz space generated by the \(N\)-function \(u(x) = \exp \{|x |\} - 1\).

MSC:

60G15	Gaussian processes
60F25	\(L^p\)-limit theorems

Keywords:

super-Gaussian random variables; rate of convergence of Baxter sums; Orlicz space