论文标题
定量限制定理通过相对对数covity
Quantitative limit theorems via relative log-concavity
论文作者
论文摘要
在本文中，我们开发了通过凸度来研究限制定理的工具。我们在概率度量$μ$和$ν$之间建立了差异的界限，以使$ν$相对于$μ$是log-concave。我们讨论了多种应用，其中包括与随机变量总和和伽马分布之间差异的几何和二项式近似值。作为特殊情况，我们获得了用于内在体积的罕见事件定律，与无限分布分布的几何相近的定量界限，以及用于矩形的二项式和泊松近似。
In this paper we develop tools for studying limit theorems by means of convexity. We establish bounds for the discrepancy in total variation between probability measures $μ$ and $ν$ such that $ν$ is log-concave with respect to $μ$. We discuss a variety of applications, which include geometric and binomial approximations to sums of random variables, and discrepancy between Gamma distributions. As special cases we obtain a law of rare events for intrinsic volumes, quantitative bounds on proximity to geometric for infinitely divisible distributions, as well as binomial and Poisson approximation for matroids.
