Subgaussian and strictly subgaussian random variable

Abstract

We study in this report the so-called Strictly Subgaussian (SSub) random variables (r.v.), which form a very interest subclass of Subgaussian (Sub) r.v., and obtain the exact exponential bounds for tail of distribution for sums of independent and disjoint such a variables, not necessary to be identical distributed, and give some new examples of SSub variables to show the exactness of our estimates. We extend also these results on the case of sums of subgaussian martingale differences, and show that the mixture of (Strictly) Subgaussian r.v. forms also (Strictly) subgaussian variable.