相关论文: Concentration for Infinitely Divisible Vectors wit…
Entropy and differential entropy are important quantities in information theory. A tractable extension to singular random variables-which are neither discrete nor continuous-has not been available so far. Here, we present such an extension…
We study a class of nonlinear non-autonomous nonlocal equations with subcritical and critical exponential nonlinearity. The involved potential can vanish at infinity.
Maximal inequalities refer to bounds on expected values of the supremum of averages of random variables over a collection. They play a crucial role in the study of non-parametric and high-dimensional estimators, and especially in the study…
We study the eigenvalues for infinitesimal generators of semigroups of composition operators acting on Hardy spaces, Bergman spaces, and the Dirichlet space. Such semigroups are induced by semigroups of holomorphic functions. Depending on…
The general relationship between an arbitrary frequency distribution and the expectation value of the frequency distributions of its samples is discussed. A wide set of measurable quantities ("invariant moments") whose expectation value…
In a recent paper the author obtained optimal bounds for the strong Gaussian approximation of sums of independent $\R^d$-valued random vectors with finite exponential moments. The results may be considered as generalizations of well-known…
We consider the problem of embedding one i.i.d.\ collection of Bernoulli random variables indexed by $\mathbb{Z}^d$ into an independent copy in an injective $M$-Lipschitz manner. For the case $d=1$, it was shown by Basu and Sly (PTRF, 2014)…
This paper is devoted to the analysis of a finite horizon discrete-time stochastic optimal control problem, in presence of constraints. We study the regularity of the value function which comes from the dynamic programming algorithm. We…
We derive exponential tail inequalities for sums of random matrices with no dependence on the explicit matrix dimensions. These are similar to the matrix versions of the Chernoff bound and Bernstein inequality except with the explicit…
Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a parametric discrete differential inclusion problem involving a real symmetric and…
We present some new results on the joint distribution of an arbitrary subset of the ordered eigenvalues of complex Wishart, double Wishart, and Gaussian hermitian random matrices of finite dimensions, using a tensor pseudo-determinant…
Lipschitz constants for the width and diameter functions of a convex body in $\mathbb R^n$ are found in terms of its diameter and thickness (maximum and minimum of both functions). Also, a dual approach to thickness is proposed.
In the paper, we provide an effective method for the Lipschitz equivalence of two-branch Cantor sets and three-branch Cantor sets by studying the irreducibility of polynomials. We also find that any two Cantor sets are Lipschitz equivalent…
We extend to infinite dimensional separable Hilbert spaces the Schur convexity property of eigenvalues of a symmetric matrix with real entries. Our framework includes both the case of linear, selfadjoint, compact operators, and that of…
We prove that solution operators of elliptic obstacle-type variational inequalities (or, more generally, locally Lipschitz continuous functions possessing certain pointwise-a.e. convexity properties) are Newton differentiable when…
The concentration of empirical measures is studied for dependent data, whose joint distribution satisfies Poincar\'{e}-type or logarithmic Sobolev inequalities. The general concentration results are then applied to spectral empirical…
We construct a differentiable locally Lipschitz function $f$ in $\mathbb{R}^{N}$ with the property that for every convex body $K\subset \mathbb{R}^N$ there exists $\bar x \in \mathbb{R}^N$ such that $K$ coincides with the set $\partial_L…
Lower and upper bounds for a given function are important in many mathematical and engineering contexts, where they often serve as a base for both analysis and application. In this short paper, we derive piecewise linear and quadratic…
We propose new statistical tests, in high-dimensional settings, for testing the independence of two random vectors and their conditional independence given a third random vector. The key idea is simple, i.e., we first transform each…
We find necessary and sufficient conditions for the free additive infinite divisibility of some free multiplicative convolutions with the Wigner, the arcsine, the free Poisson and other distributions, including explicit examples.