Relations between exponential tails, moments and moment generating functions for random variables and vectors
arXiv:1701.01901
Abstract
We offer in this paper the non-asymptotical pairwise bilateral exact up to multiplicative constants interrelations between exponential decreasing tail behavior, moments (Grand Lebesgue Spaces) norm and moment generating functions norm for random variables and vectors (r.v.).
arXiv commentarXiv admin note: text overlap with arXiv:1510.08945, arXiv:1510.04182
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- A note about associate and dual spaces to the Grand Lebesgue ones
- Grand Lebesgue Spaces are really Banach algebras relative to the convolution on unimodular locally compact groups
- Asymptotic and non-asymptotic estimates for multivariate Laplace integrals
- Exponential tail estimates in the Law of Ordinary Logarithm (LOL) for arrays of random variables
- Moment and tail estimation for U-statistics with positive kernels
- Grand Lebesgue Spaces norm estimates for multivariate functional operations
- Moment and tail estimates and Banach space valued Non-Central Limit Theorem (NCLT) for sums of multi-indexed random variables, processes and fields
- Quasi Grand Lebesgue Spaces
- Method Monte-Carlo for solving of non-linear integral equations