Related papers: Concentration Inequalities for Multinoulli Random …
We study the approximation of non-negative multi-variate couplings in the uniform norm while matching given single-variable marginal constraints.
In this short note we show an equivalence between Sobolev type inequalities and so called isocapacitary inequalities in the context of a large class of nonlinear Dirichlet forms, their associated Dirichlet spaces and their associated…
In many areas of engineering and sciences, decision rules and control strategies are usually designed based on nominal values of relevant system parameters. To ensure that a control strategy or decision rule will work properly when the…
We study boundary regularity for the inhomogeneous Dirichlet problem for $2s$-stable operators in generalized H\"older spaces. Moreover, we provide explicit counterexamples that showcase the sharpness of our results. Our approach directly…
In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of Bernoulli numbers of the second kind.
For functions of independent random variables, various upper and lower variance bounds are revisited in diverse settings. These are then specialized to the Bernoulli, Gaussian, infinitely divisible cases and to Banach space valued random…
Perturbations of super Poincar\'e and weak Poincar\'e inequalities for L\'evy type Dirichlet forms are studied. When the range of jumps is finite our results are natural extensions to the corresponding ones derived earlier for diffusion…
We prove extensions of classical concentration inequalities for random variables which have $\alpha$-subexponential tail decay for any $\alpha \in (0,2]$. This includes Hanson--Wright type and convex concentration inequalities. We also…
We study a variational problem for the first Schrodinger eigenvalue on closed Riemannian surfaces. More precisely, we explore concentration-compactness properties of sequences formed by its extremal potentials.
We introduce a series of numbers which serve as a generalization of Bernoulli, Euler numbers and binomial coefficients. Their properties are applied to solve a probability problem and suggest a statistical test for independence and…
We consider a multinomial distribution, where the number of cells increases and the cell-probabilities decreases as the number of observations grows. The probabilities of large deviations of statistics, which has form of a sum of Borel…
In this work, a generalization of the well known Bernoulli inequality is obtained by using the theory of discrete fractional calculus. As far as we know our approach is novel.
We study the existence and the properties of solutions to the Dirichlet problem for uniformly elliptic second-order Hamilton-Jacobi-Bellman operators, depending on the principal eigenvalues of the operator.
The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the…
Using, as main tool, the convergence theorem for discrete martingales and the mean value property of harmonic functions we solve, a particular case of, Dirichlet problem.
Let $\{{\bf \mathcal{Z}}_n:n\geq 1\}$ be a sequence of i.i.d. random probability measures. Independently, for each $n\geq 1$, let $(X_{n1},\ldots, X_{nn})$ be a random vector of positive random variables that add up to one. This paper…
We prove an elementary yet useful inequality bounding the maximal value of certain linear programs. This leads directly to a bound on the martingale difference for arbitrarily dependent random variables, providing a generalization of some…
The main goal of this paper is to answer question 1.10 and settle conjecture 1.11 of Benjamini-Lyons-Schramm [BLS99] relating harmonic Dirichlet functions on a graph to those of the infinite clusters in the uniqueness phase of Bernoulli…
We revisit Hardy's inequality in the scope of regular Dirichlet forms following an analytical method. We shall give an alternative necessary and sufficient condition for the occurrence of Hardy's inequality. A special emphasis will be given…
We establish deviation inequalities for the maxima of partial sums of a martingale differences sequence, and of a strictly stationary orthomartingale random field. These inequalities can be used to establish complete convergence of…