Related papers: Bernstein- and Markov-type inequalities

We derive new concentration bounds for time averages of measurement outcomes in quantum Markov processes. This generalizes well-known bounds for classical Markov chains which provide constraints on finite time fluctuations of time-additive…

We study a variant of the majorization relation. In particular we consider inequalities involving some Schur-concave symmetric polynomials related to the multinomial expansion. We also discuss how these topics were motivated by conjectures…

In this paper, we consider the poly-Bernoulli numbers and polynomials of the second kind and presents new and explicit formulae for calculating the poly-Bernoulli numbers of the second kind and the Stirling numbers of the second kind.

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

Two articles published by Information Science discuss the derivatives of interval functions, in the sense of Svetoslav Markov. The authors of these articles tried to characterize for which functions and points such derivatives exist.…

We study the relationship between sampling sequences in infinite dimensional Hilbert spaces of analytic functions and Marcinkiewicz-Zygmund inequalities in subspaces of polynomials. We focus on the study of the Hardy space and the Bergman…

A general class of Markov processes with a local interaction is introduced, which includes exclusion and Kawasaki processes as a very particular case. Bernoulli invariant measures are found for this class of processes.

A class of generalized Schr\"{o}dinger problems in bounded domain is studied. A complete overview of the set of solutions is provided, depending on the values assumed by parameters involved in the problem. In order to obtain the results, we…

We analyze certain stationary fields with linear regressions and quadratic conditional variances. This classic probabilistic problem leads somewhat unexpectedly to stationary Markov processes closely tied to non-commutative probability…

We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.

A new probalistic approach to general relativistic kinetic theory is proposed. The general relativistic Boltzmann equation is linked to a new Markov process in a completely intrinsic way. This treatment is then used to prove the causal…

We give direct and inverse theorems for the weighted approximation of functions with inner singularities by combinations of Bernstein polynomials.

Inequalities are important features in the context of sequences of numbers and polynomials. The Bessenrodt--Ono inequality for partition numbers and Nekrasov--Okounkov polynomials has only recently been discovered. In this paper we study…

By using definition of Golden derivative, corresponding Golden exponential function and Fibonomial coefficients, we introduce generating functions for Bernoulli-Fibonacci polynomials and related numbers. Properties of these polynomials and…

We use M\"obius inversion and the Bernoulli polynomials to prove inequalities between the logarithmic summatory function of the M\"obius function and weighted averages of its ordinary summatory function.

In this paper, new versions of Chebyshev's, Minkowski's and Holder's type inequalities are studied by using a monotone measure-base universal integral on an arbitrary measurable space. This paper generalizes some previous results obtained…

In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

We summarize results concerning the Bernstein property of differential equations.

We define the notion of Bernstein measures and Bernstein approximations over general convex polytopes. This generalizes well-known Bernstein polynomials which are used to prove the Weierstrass approximation theorem on one dimensional…

We consider semiclassical orthogonal polynomials on the unit circle associated with a weight function that satisfy a Pearson-type differential equation involving two polynomials of degree at most three. Structure relations and difference…