相关论文: Sup-sums principles for F-divergence, Kullback--Le…
We present a new lower bound on the differential entropy rate of stationary processes whose sequences of probability density functions fulfill certain regularity conditions. This bound is obtained by showing that the gap between the…
There are many information and divergence measures exist in the literature on information theory and statistics. The most famous among them are Kullback-Leibler (1951) relative information and Jeffreys (1951) J-divergence. Sibson (1969)…
This paper presents different approaches, based on functional inequalities, to study the speed of convergence in total variation distance of ergodic diffusion processes with initial law satisfying a given integrability condition. To this…
In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special…
We present theoretical properties of the log-concave maximum likelihood estimator of a density based on an independent and identically distributed sample in $\mathbb{R}^d$. Our study covers both the case where the true underlying density is…
Kullback-Leibler relative-entropy, in cases involving distributions resulting from relative-entropy minimization, has a celebrated property reminiscent of squared Euclidean distance: it satisfies an analogue of the Pythagoras' theorem. And…
Ergodic theory includes several notions of entropy for probability-preserving actions of countable groups. These include Kolmogorov--Sinai entropy based on F\o lner sequences for amenable groups, entropy defined using a random ordering of…
Uniform upper bounds and the asymptotic expansion with an explicit remainder term are established for the Macdonald function $K_{i\tau}(x)$. The results can be applied, for instance, to study the summability of the divergent…
We prove that an inner function has finite $\mathcal{L} (p)$-entropy if and only if its accumulated M\"obius distortion is in $L^p$, $0<p<\infty$. We also study the support of the positive singular measures such that their corresponding…
In this paper, we propose extensions for the classical Kummer test, which is a very far-reaching criterion that provides sufficient and necessary conditions for convergence and divergence of series of positive terms. Furthermore, we present…
The concept of classical $f$-divergences gives a unified framework to construct and study measures of dissimilarity of probability distributions; special cases include the relative entropy and the R\'enyi divergences. Various quantum…
There are currently two main, continuum models of entropy: a 'reversible', Clausius entropy model and an 'irreversible', Onsager-Prigogine entropy model. It is shown that the equations of the 'reversible' and the 'irreversible' entropy…
The Kullback-Leibler (KL) divergence is a fundamental equation of information theory that quantifies the proximity of two probability distributions. Although difficult to understand by examining the equation, an intuition and understanding…
In the study of non-equilibrium statistical mechanics, Ruelle derived explicit formulae for entropy production of smooth dynamical systems. The vanishing or strict positivity of entropy production is determined by the {\it entropy formula…
We derive a closed-form solution for the Kullback-Leibler divergence between two Fr\'echet extreme-value distributions. The resulting expression is rather simple and involves the Euler-Mascheroni constant.
Indicator functions mentioned in the title are constructed on an arbitrary nondiscrete locally compact Abelian group of finite dimension. Moreover, they can be obtained by small perturbation from any indicator function fixed beforehand. In…
Let $D$ be an indefinite quaternion division algebra over $\mathbb{Q}$. We approach the problem of bounding the sup-norms of automorphic forms $\phi$ on $D^\times(\mathbb{A})$ that belong to irreducible automorphic representations and…
Minimization problems with respect to a one-parameter family of generalized relative entropies are studied. These relative entropies, which we term relative $\alpha$-entropies (denoted $\mathscr{I}_{\alpha}$), arise as redundancies under…
A sum rule relative to a reference measure on R is a relationship between the reversed Kullback-Leibler divergence of a positive measure on R and some non-linear functional built on spectral elements related to this measure (see for example…
Many complex systems are characterized by non-Boltzmann distribution functions of their statistical variables. If one wants to -- justified or not -- hold on to the maximum entropy principle for complex statistical systems (non-Boltzmann)…