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In this communication, we describe some interrelations between generalized $q$-entropies and a generalized version of Fisher information. In information theory, the de Bruijn identity links the Fisher...
In this paper a simple proof of the Chebyshev's inequality for random vectors obtained by Chen (arXiv:0707.0805v2, 2011) is obtained. This inequality gives a lower bound for the percentage of the popu...
We present a graphical approach to deriving inequality constraints for directed acyclic graph (DAG) models, where some variables are unobserved. In particular we show that the observed distribution of...
We investigate a one-parameter family of probability densities (related to the Pareto distribution, which describes many natural phenomena) where the Cram´er-Rao inequality provides no informa...
This paper presents a study of the large-sample behavior of the posterior distribution of a structural parameter which is partially identified by moment inequalities. The posterior density is derive...
Chernoff proves an inequality using Hemite polynomials. Here we prove and generalize this inequality using Cauchy - Schwartz inequality and Fubini equality.
This note contains the proof of a decoupling ineqnality for multilinear functions of symmetric B-valued stable random vectors.
Jensen's inequality for Schwarz maps in von Neumann algebras。
Extensions of Chebychev's inequality with applications。
Using a probabilistic technique we obtain upper and lower estimates for the Poisson kernels of the second order diflerential operators on a homogeneous manifold of negative curvature. Our results i...
We establish a logarithmic Sobolev inequality for a one- -dimensional multivalued stochastic differential equation associated with the subdillerential of a convex lower semicontinuous function, usin...
In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different proof of the main technical lemma that guarantees the existence of a certain kernel....
The inequality of Vapnik and Chervonenkis controls the expectation of the function by its sample average uniformly over a VC-major class of functions taking into account the size of the expectation...
Let $X=(X_t)_{tgeq 0}$ be a martingale and $H=(H_t)_{tgeq 0}$ be a predictable process taking values in $[-1,1]$. Let $Y$ denote the stochastic integral of $H$ with respect to $X$. We show that $$ ||s...
The purpose of this work is to study some possible application of FKG inequality to the Brownian motion and to Stochastic Differential Equations. We introduce a special ordering on the Wiener space an...

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