On the existence of exponential moments of norms of random elements from the spaces \(\text{sub}_ \varphi (\Omega)\). (English. Ukrainian original) Zbl 0863.60038

Velikoivanenko, G. I.

Theory Probab. Math. Stat. 50, 61-65 (1995); translation from Teor. Jmovirn. Mat. Stat. 50, 61-65 (1994).

Summary: \((B,|\cdot|)\)-valued random elements \(X\) from the space \(\text{sub}_\varphi\), where \((B,|\cdot|)\) is a Banach space, are considered. The exponential integrability of a random vector \(X\), that is, the belonging of the random variable \(|X|\) to the Orlicz space generated by the function \(u(x)=\text{exp}\{\varphi^*(x)\}-1\) in the case \(B={\mathbf L}_p\), is demonstrated.

MSC:

60G15	Gaussian processes
60G17	Sample path properties
62E17	Approximations to statistical distributions (nonasymptotic)

Keywords:

exponential integrability; Orlicz space