一个锐相关不等式及其对几乎必然局部极限定理的应用
A sharp correlation inequality with an application to almost sure local limit theorem
摘要：
证明了独立同分布和的一个新的相关不等式。平方可积〔的〕格点分布随机变量。我们还应用它建立了取值于任意格上的平方可积〔的〕随机变量的几乎必然局部极限定理。这推广了最近与Antonini-Giuliano在稍强的绝对矩假设下（$2+u$与$u>0$的阶）共同获得的类似结果。用于治疗$u>0$病例的方法在发生$u=0$时失效。麦克唐纳的概念的伯努利部分的随机变量是用来在一个重要的方式来弥补这一点。
英文摘要：
We prove a new sharp correlation inequality for sums of i.i.d. square integrable lattice distributed random variables. We also apply it to establish an almost sure local limit theorem for iid square integrable random variables taking values in an arbitrary lattice. This extends a recent similar result jointly obtained with Antonini-Giuliano, under a slightly stronger absolute moment assumption (of order $2+u$ with $u>0$). The approach used to treat the case $u>0$ breaks down when $u=0$. MacDonald's concept of the Bernoulli part of a random variable is used in a crucial way to remedy this.
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