相关论文: Jensen's inequality for conditional expectations
Jensen inequalities for positive linear maps of Choi and Hansen-Pedersen type are established for a large class of operator/matrix means. These results are also extensions of the Minkowski determinantal inequality. To this end we develop…
An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.
In this paper, we introduce a new type of backward stochastic differential equations (BSDEs), called conditional expectation BSDEs, whose drivers depend not only on the value of the solutions but also on their conditional expectations with…
We provide a function class which is useful to distinguish central and non-central elements of a $C^*$-algebra in the following sense: for each element $f$ of this function class, a self-adjoint element $a$ of a $C^*$-algebra is central if…
In this paper, with the notion of independent identically distributed (IID) random variables under sublinear expectations introduced by Peng [7-9], we investigate moment bounds for IID sequences under sublinear expectations. We can obtain a…
We develop criteria to guarantee uniqueness of the C$^*$-norm on a *-algebra $\mathcal{B}$. Nontrivial examples are provided by the noncommutative algebras of $\mathcal{C}$-valued functions $\mathcal{S}_J^\mathcal{C}(\mathbb{R}^n)$ and…
There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…
It is known that functions in a Sobolev space with critical exponent embed into the space of functions of bounded mean oscillation, and therefore satisfy the John-Nirenberg inequality and a corresponding exponential integrability estimate.…
We prove a sharp inequality conjectured by Bobkov on the measure of dilations of Borel sets in $\mathbb{R}^n$ by a $s$-concave probability. Our result gives a common generalization of an inequality of Nazarov, Sodin and Volberg and a…
We survey several significant results on the Bohr inequality and presented its generalizations in some new approaches. These are some Bohr type inequalities of Hilbert space operators related to the matrix order and the Jensen inequality.…
Several numerical radius inequalities in the framework of $C^*$-algebras are proved in this paper. These results, which are based on an extension of Buzano inequality for elements in a pre-Hilbert $C^*$-module, generalize earlier numerical…
In this paper, a new lemma is proved and inequalities of Simpson type are established for co-ordinated convex functions and bounded functions.
We consider certain positive definite functions on a finitely generated free group G that are defined with respect to a given basis in terms of word length and the number of negative-to-positive generator exponent switches. Some of these…
The separate tasks of denoising, least squares expectation, and manifold learning can often be posed in a common setting of finding the conditional expectations arising from a product of two random variables. This paper focuses on this more…
Let $\mathscr{M}$ be a finite von Neumann algebra with a faithful normal tracial state $\tau$ and $\mathfrak{A}$ be a finite subdiagonal subalgebra of $\mathscr{M}$ with respect to a $\tau$-preserving faithful normal conditional expectation…
Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the…
The purpose of this paper is to establish several necessary and sufficient conditions to ensure the validity of a general functional inequality in terms of generalized quasi-arithmetic means. In particular cases, we consider H\"older-,…
The main purpose of this paper is to construct *-representations from unbounded C$^*$-seminorms on partial *-algebras and to investigate their *-representations.
In this paper, we present a generalization of the Huygens types inequalities involving Bessel and modified Bessel functions of the first kind.
Some sharp inequalities of Gruss type for sequences of vectors in real or complex inner product spaces are obtained. Applications for Jensen's inequality for convex functions defined on such spaces are also provided.