A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)
Functional Analysis
2012-10-04 v1 Probability
Abstract
We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate also a conjugate to offered spaces and obtain some embedding theorems. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables).
Keywords
Cite
@article{arxiv.1210.1168,
title = {A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)},
author = {E. Ostrovsky and L. Sirota},
journal= {arXiv preprint arXiv:1210.1168},
year = {2012}
}