Related papers: Bernstein-Markov: a survey
In this paper, we propose a new approach for deriving probabilistic inequalities. Our main idea is to exploit the information of underlying distributions by virtue of the monotone likelihood ratio property and Berry-Essen inequality.…
In this paper, some new Gronwall type inequalities involving iterated integrals are given.
In this article, recent progress on ML-randomness with respect to conditional probabilities is reviewed. In particular a new result of conditional randomness with respect to mutually singular probabilities are shown, which is a…
This article is a lecture note on the potential theory of (possibly non-reversible) Markov processes and on the connection of this theory with quantitative analysis of the metastability of stochastic processes.
A simple model of the new notion of "Markov up" processes is proposed; its positive recurrence and ergodic properties are shown under the appropriate conditions.
The goal of the present paper is to discuss new transport inequalities for convex measures. We retrieve some dimensional forms of Brascamp-Lieb inequalities. We also give some quantitative forms involving the Wasserstein's distances.
We discuss recent versions of the Brunn-Minkowski inequality in the complex setting, and use it to prove the openness conjecture of Demailly and Koll\'ar.
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
We present a short proof of a conjecture proposed by I. Ra\c{s}a (2017), which is an inequality involving basic Bernstein polynomials and convex functions. This proof was given in the letter to I. Ra\c{s}a (2017). The methods of our proof…
We report in this survey some new results concerning noncommutative Chern characters: construction and the cases when they are exactly computed. The major result indicates some clear relation of these noncommutative objects and their…
In this paper, a new generalized Bernstein-Bezier type operators is constructed.The estimates of the moments of these operators are investigated. The rate of convergence in terms of modulus of continuity is given. Then, the equivalent…
We present unified approach to different recent entanglement criteria. Although they were developed in different ways, we show that they are all applications of a more general principle given by the Cauchy-Schwarz inequality. We explain…
Two approaches to hypothesis testing, e-value testing and Bayes risk minimisation, both invoke Markov's inequality to control error probabilities. They differ in which distribution certifies the unit-moment condition: the null for Type I…
Utilizing the notion of positive multilinear mappings, we give some matrix inequalities. In particular, Choi--Davis--Jensen and Kantorovich type inequalities including positive multilinear mappings are presented.
In a recent paper [T. C. Ralph, W. J. Munro, R. E. S. Polkinghorne, Phys. Rev. Lett. 85, 2035 (2000)], the authors propose a test for Bell's inequalities based on quadrature measurements for a correlated parametric source. We present here a…
Some new sufficient conditions for the weighted Chebyshev's inequality for real numbers to hold are provided.
We provide a sharp nonasymptotic analysis of the rates of convergence for some standard multivariate Markov chains using spectral techniques. All chains under consideration have multivariate orthogonal polynomial as eigenfunctions. Our…
Improved rates of convergence for ergodic Markov chains and relaxed conditions for them, as well as analogous convergence results for some non-homogeneous Markov chains are studied. The setting from the previous works is extended. Examples…
The aim of this note is to prove a semi-discrete Gruss-Voronovskaya-type estimate for Bernstein-Kantorovich polynomials. Also, as a consequence, a perturbed Gruss-type estimate is obtained.
Given a matrix of distribution functions and a quasi-stochastic matrix, i.e. an irreducible nonnegative matrix with maximal eigenvalue one and associated unique positive left and right eigenvectors, the article studies the properties of an…