Divergence of an integral of a process with small ball estimate

计算关于全变差距离和卡方散度球的下期望

Computing lower expectations with respect to total variation distance and chi-squared divergence balls

针对有限集上的概率质量函数，推导了在全变差距离球和卡方散度球下的下期望的闭式表达式。

Sup-sums principles for F-divergence, Kullback--Leibler divergence, and new definition for t-entropy

The article presents new sup-sums principles for integral F-divergence for arbitrary convex function F and arbitrary (not necessarily positive and absolutely continuous) measures. As applications of these results we derive the corresponding sup-sums principle for Kullback--Leibler divergence and work out new `integral' definition for t-entropy explicitly establishing its relation to Kullback--Leibler divergence.

Levy Gamma积分的有序发散

Orderly divergence of Levy Gamma integrals

本文研究原本不可积函数的加权随机Gamma积分的极限定理，指出在单调性缺失时会出现离散情形所没有的新特征。

关于关于 Hermite 过程的散度积分的 $1/H$-变差的探讨

On the $1/H$-variation of the divergence integral with respect to a Hermite process

本文定义了关于 Hermite 过程的随机被积函数的散度型积分，并证明该积分具有有限的 $1/H$-变差。

On $f$-Divergences: Integral Representations, Local Behavior, and Inequalities

This paper is focused on $f$-divergences, consisting of three main contributions. The first one introduces integral representations of a general $f$-divergence by means of the relative information spectrum. The second part provides a new approach for the derivation of $f$-divergence inequalities, and it exemplifies their utility in the setup of Bayesian binary hypothesis testing. The last part of this paper further studies the local behavior of $f$-divergences.

On the $\frac{1}{H}$-variation of the divergence integral with respect to fractional Brownian motion with Hurst parameter $H < 1/2$

In this paper, we study the $\frac{1}{H}$-variation of stochastic divergence integrals $X_t = \int_0^t u_s δB_s$ with respect to a fractional Brownian motion $B$ with Hurst parameter $H < \frac{1}{2}$. Under suitable assumptions on the process u, we prove that the $\frac{1}{H}$-variation of $X$ exists in $L^1(Ω)$ and is equal to $e_H \int_0^T|u_s|^H ds$, where $e_H = \mathbb{E}|B_1|^H$. In the second part of the paper, we establish an integral representation for the fractional Bessel Process $\|B_t\|$, where $B_t$ is a $d$-dimensional fractional Brownian motion with Hurst parameter $H < \frac{…