English
Related papers

Related papers: Jensen's inequality for conditional expectations

200 papers

In this paper we consider a sequence of random variables with mean uncertainty in a sublinear expectation space. Without the hypothesis of identical distributions, we show a new central limit theorem under the sublinear expectations.

Probability · Mathematics 2015-05-19 Min Li , Yufeng Shi

The present paper is devoted to the study of Jensen-Mercer-type inequalities. Our results generalize and improve some earlier results in the literature.

Classical Analysis and ODEs · Mathematics 2019-05-07 Hamid Reza Moradi , Shigeru Furuichi

Motivated by a recent result on finite-dimensional Hilbert spaces, we prove a Jensen's inequality for partial traces in semifinite von Neumann algebras. We also prove a similar inequality in the framework of general (non-tracial) von…

Operator Algebras · Mathematics 2026-03-11 Mizanur Rahaman , Lyudmila Turowska

The well known Jensen inequality, holds true for every convex functions. However, we found that it is possible to apply it to some problems related to nonconvex functions for which Jensen's inequality holds true locally. Having considered a…

General Mathematics · Mathematics 2014-12-18 Adilsultan Lepes

It is well known that the traditional Jensen inequality is proved by lower bounding the given convex function, $f(x)$, by the tangential affine function that passes through the point $(E\{X\},f(E\{X\}))$, where $E\{X\}$ is the expectation…

Information Theory · Computer Science 2023-05-17 Neri Merhav

Some mathematical inequalities among various weighted means are studied. Inequalities on weighted logarithmic mean are given. Besides, the gap in Jensen's inequality is studied as a convex function approach. Consequently, some non-trivial…

Classical Analysis and ODEs · Mathematics 2022-11-08 Shigeru Furuichi , Kenjiro Yanagi , Hamid Reza Moradi

In this note we give a recipe which describes upper and lower bounds for the Jensen functional under superquadraticity conditions. Some results involve the Chebychev functional. We give a more general definition of these functionals and…

Classical Analysis and ODEs · Mathematics 2015-11-09 Flavia-Corina Mitroi-Symeonidis , Nicuşor Minculete

In this paper we develop a general method for improving Jensen-type inequalities for convex and, even more generally, for piecewise convex functions. Our main result relies on the linear interpolation of a convex function. As a consequence,…

Classical Analysis and ODEs · Mathematics 2016-10-06 Daeshik Choi , Mario Krnić , Josip Pecarić

A considerable amount of literature in the theory of inequality is devoted to the study of Jensen's and Young's inequality. This article presents a number of new inequalities involving the log-convex functions and the geometrically convex…

Classical Analysis and ODEs · Mathematics 2022-02-10 Shigeru Furuichi , Hamid Reza Moradi , Supriyo Dutta

We establish several operator versions of the classical Aczel inequality. One of operator versions deals with the weighted operator geometric mean and another is related to the positive sesquilinear forms. Some applications including the…

Functional Analysis · Mathematics 2012-03-22 Mohammad Sal Moslehian

The question of which separable C*-algebras have abelian central sequence algebras was raised and studied by Phillips ([Ph88]) and Ando-Kirchberg ([AK14]). In this paper we give a complete answer to their question: A separable C*-algebra…

Operator Algebras · Mathematics 2022-04-08 Dominic Enders , Tatiana Shulman

This paper proposes a new sharpened version of the Jensen's inequality. The proposed new bound is simple and insightful, is broadly applicable by imposing minimum assumptions, and provides fairly accurate result in spite of its simple form.…

Statistics Theory · Mathematics 2017-10-26 J. G. Liao , Arthur Berg

In this paper we extend the notion of g-evaluation, in particular g-expectation, to the case where the generator g is allowed to have a quadratic growth. We show that some important properties of the g-expectations, including a…

Probability · Mathematics 2009-12-19 Jin Ma , Song Yao

In this article we present a Bernstein inequality for sums of random variables which are defined on a spatial lattice structure. The inequality can be used to derive concentration inequalities. It can be useful to obtain consistency…

Statistics Theory · Mathematics 2017-12-06 Eduardo Valenzuela-Domínguez , Johannes T. N. Krebs , Jürgen E. Franke

The primary goal of this paper is to improve the operator version of Jensen inequality. As an application, we provide an improvement for the celebrated Ando's inequality. Additionally, we give a tight bound for the operator H\"older…

Functional Analysis · Mathematics 2021-04-27 Hamid Reza Moradi , Shigeru Furuichi , Mohammed Sababheh

In this paper we prove results on the difference between a normalized Jensen functional and the sum of other normalized Jensen functionals for convex function.

Functional Analysis · Mathematics 2024-05-27 Shoshana Abramovich

The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gr\"{u}ss Inequality. It has been reported in the literature that fragmentation (or…

Systems and Control · Computer Science 2012-04-06 Corentin Briat

The continuity of conditional expectation on Orlicz spaces is investigated. Indeed, we provide some necessary and sufficient conditions on a sequence $\{\mathcal{A}_n\}_{n\in\mathbb{N}}$ of $\sigma$-subalgebras for $L^{\varphi}$-convergence…

Functional Analysis · Mathematics 2025-10-28 A. Hosseini , Y. Estaremi

In this paper, we state some characterizations of $h$-convex function is defined on a convex set in a linear space. By doing so, we extend the Jensen-Mercer inequality for $h$-convex function. We will also define $h$-convex function for…

Functional Analysis · Mathematics 2020-03-31 M. Abbasi , A. Morassaei , F. Mirzapour

We give a concentration inequality based on the premise that random variables take values within a particular region. The concentration inequality guarantees that, for any sequence of correlated random variables, the difference between the…

Probability · Mathematics 2020-02-21 Go Kato