相关论文: Jensen's inequality for conditional expectations

In 2014, Rieffel introduced norms on certain unital C*-algebras built from conditional expectations onto unital C*-subalgebras. We begin by showing that these norms generalize the Frobenius norm, and we provide explicit formulas for certain…

Motivated by some recently established operator Jensen-type inequalities related to a usual convexity, in the present paper we derive several more accurate operator Jensen-type inequalities for certain subclasses of convex functions. More…

In this paper the Jessen's type inequality for normalized positive $C_0$-semigroups is obtained. An adjoint of Jessen's type inequality has also been derived for the corresponding adjoint-semigroup, which does not give the analogous results…

This article presents a theoretical study of uncertainty functionals on general measurable spaces. These functionals are fundamental in experimental design and global sensitivity analysis, where they are used to quantify variability and…

In this paper we deal with improvement of Jensen, Jensen-Steffensen's and Jensen's functionals related inequalities for uniformly convex, phi-convex and superquadratic functions.

In this paper we improve results related to Normalized Jensen Functional for convex functions and Uniformly Convex Functions.

Classically, Jensen's Inequality asserts that if $X$ is a compact convex set, and $f:K\to \mathbb{R}$ is a convex function, then for any probability measure $\mu$ on $K$, that $f(\text{bar}(\mu))\le \int f\;d\mu$, where $\text{bar}(\mu)$ is…

In this note we describe some results concerning upper and lower bounds for the Jensen functional. We use several known and new results to shed light on the concepts of superterzatic functions.

In this paper, using some aspects of convex functions, we refine discrete Jensen's inequality via weight functions. Then, using these results, we give some applications in different abstract spaces and obtain some new interesting…

We investigate how basic probability inequalities can be extended to an imprecise framework, where (precise) probabilities and expectations are replaced by imprecise probabilities and lower/upper previsions. We focus on inequalities giving…

We investigate monotone operator functions of several variables under a trace or a trace-like functional. In particular, we prove the inequality \tau(x_1... x_n)\le\tau(y_1... y_n) for a trace \tau on a C^*-algebra and abelian n-tuples…

We show that the existence of a continuous conditional expectation from a Fell bundle to a Fell subbundle implies that the full cross-sectional C*-algebra of the subbundle is contained in the full cross-sectional C*-algebra of the bundle,…

We generalize McDiarmid's inequality for functions with bounded differences on a high probability set, using an extension argument. Those functions concentrate around their conditional expectations. We further extend the results to…

We prove certain type symmetric inequalities in $\textbf{R}^{2}$ and $\textbf{R}^3$, that ocur in many problems of analysis. These inequalities are generalizations of the Jensen's inequality from one variable to two and three variables

In this paper, we introduce the notion of conditional $h$-convex functions and we prove an operator version of the Jensen inequality for conditional $h$-convex functions. Using this type of functions, we give some refinements for Ky-Fan's…

Sublinear functionals of random variables are known as sublinear expectations; they are convex homogeneous functionals on infinite-dimensional linear spaces. We extend this concept for set-valued functionals defined on measurable set-valued…

As an extension of a central limit theorem established by Svante Janson, we prove a Berry-Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically…

We study a family of inequalities on pairs of measure spaces involving functions defined on product domains. Our main result establishes a Jensen-type inequality under a general product-measure framework, extending classical inequalities…

We introduce a quite large class of functions (including the exponential function and the power functions with exponent greater than one), and show that for any element $f$ of this function class, a self-adjoint element $a$ of a…

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…