论文标题
mod-poisson近似方案和高阶陈·斯坦不平等现象
Mod-Poisson approximation schemes and higher-order Chen-Stein inequalities
论文作者
论文摘要
在本文中，我们提供了Chen-Stein不等式的泊松近似值，以两种方式的独立Bernoulli随机变量总和的总变化距离。我们证明，我们可以使用明确构造的签名或正概率度量来提高收敛速率（因此近似质量），并且我们可以将设置扩展到可能因素的随机变量。允许这种情况的框架是Mod-Poisson收敛的框架，更精确地是那些Mod-Poisson Convergent序列，其残基函数可以表示为一系列基本对称函数的专业化。这种组合重新制定使我们拥有一个一般和统一的框架，在该框架中，我们可以符合独立的Bernoulli随机变量和其他示例的经典设置，例如来自概率数字理论和随机排列。
In this article, we provide an extension of the Chen-Stein inequality for Poisson approximation in the total variation distance for sums of independent Bernoulli random variables in two ways. We prove that we can improve the rate of convergence (hence the quality of the approximation) by using explicitly constructed signed or positive probability measures, and that we can extend the setting to possibly dependent random variables. The framework which allows this is that of mod-Poisson convergence, and more precisely those mod-Poisson convergent sequences whose residue functions can be expressed as a specialization of the generating series of elementary symmetric functions. This combinatorial reformulation allows us to have a general and unified framework in which we can fit the classical setting of sums of independent Bernoulli random variables as well as other examples coming e.g. from probabilistic number theory and random permutations.
