Grand Lebesgue norm estimation for binary random variables, with applications

Eugene Ostrovsky; Leonid Sirota

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arXiv · 1507.07576

Grand Lebesgue norm estimation for binary random variables, with applications

Eugene Ostrovsky·Leonid Sirota

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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.

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Eugene Ostrovsky, Leonid Sirota. 2015-07-27. Grand Lebesgue norm estimation for binary random variables, with applications. https://arxiv.org/abs/1507.07576

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