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

Yu. V. Kozachenko; E. Ostrovsky; L. Sirota

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arXiv · 1710.05260

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

Yu. V. Kozachenko·E. Ostrovsky·L. Sirota

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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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Yu. V. Kozachenko, E. Ostrovsky, L. Sirota. 2017-10-15. Equivalence between tails, Grand Lebesgue Spaces and Orlicz norms for random variables without Cramer's condition. https://arxiv.org/abs/1710.05260

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