English

Grand Lebesgue norm estimation for binary random variables, with applications

Probability 2015-07-29 v1

Abstract

We calculate the so-called Rademacher's Grand Lebesgue Space norm for a centered (shifted) indicator (Bernoulli's, binary) random variable. This norm is optimal for the centered and bounded random variables (r.v.). Using this result we derive a very simple bilateral sharp exponential tail estimates for sums of these variables, not necessary to be identical distributed, under non-standard norming, and give some examples to show the exactness of our estimates.

Keywords

Cite

@article{arxiv.1507.07576,
  title  = {Grand Lebesgue norm estimation for binary random variables, with applications},
  author = {Eugene Ostrovsky and Leonid Sirota},
  journal= {arXiv preprint arXiv:1507.07576},
  year   = {2015}
}
R2 v1 2026-06-22T10:19:55.212Z