Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition

Abstract

We offer in this paper the non-asymptotical pairwise bilateral exact up to multiplicative constants interrelations between the tail behavior, moments (Grand Lebesgue Spaces) norm and Orlicz's norm for random variables (r.v.), which does not satisfy in general case the Cramer's condition.

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Cited by in corpus (3)

• Restricted version of Grand Lebesgue Spaces
• Tail estimations for functions belonging to Grand Lebesgue Spaces builded on the set with infinite measure
• Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables