- On the East inequality in the space of sub-Gaussian random variables of rank p (arXiv)
Author: Krzysztof Zadzikowski
Summary: If p>1, the function φp(x)=x2/2 if |x|≤1, φp(x)=1/p|x|p−1/p if |x|>1 Let's say +1/2. . For a random variable ξ, let τφp(ξ) denote inf{c≥0:∀λ∈RlnEexp(λξ)≤φp(cλ)}. τφp is the norm of the φp sub-Gaussian random variable in the space Subφp(Ω)={ξ:τφp(ξ)<∞}, which is called the {\it sub-Gaussian distribution of rank p random variables}. If p=2, we get a classical sub-Gaussian random variable. The East inequality gives an estimate of the probability of deviation of a zero-mean martingale (ξn)n≥0 by finite increments from zero. In classical form, it is assumed that ξ0=0. In this paper, we present a version of the East inequality under the assumption that ξ0 is an arbitrary sub-Gaussian of a random variable of rank p.
2. On an improved version of Higashi-Heffding inequality applied to information theory (arXiv)
Author: Yigal Sason
Abstract: This is a research paper containing the author's own results on a sophisticated version of the Azuma-Hoeffding inequality, including several examples related to information theory. This research evolved into a joint paper with his Maxim Raginsky on arXiv:1212.4663v3.
