论文标题
关于负依赖的随机过程的尾巴琐事
On Tail Triviality of Negatively Dependent Stochastic Processes
论文作者
论文摘要
我们证明，与“可总结协方差”的伯努利随机变量的每个负相关的序列都有一个微不足道的尾巴场。这种结果的必然是强烈的雷利过程的尾巴。这是由于里昂引起的结果的概括，该结果为离散的确定过程建立了尾巴琐碎。我们还研究了负相关的高斯和高斯阈值过程的尾巴行为。我们表明，尽管这些过程一般不满足可总结的协方差属性，但这些过程是微不足道的。此外，我们构建并非强烈的瑞利（Rayleigh）构建负相关的高斯阈值矢量。这确定了一个自然相关的措施的自然家族，这不是强烈的雷利措施类别的子集。
We prove that every negatively associated sequence of Bernoulli random variables with "summable covariances" has a trivial tail sigma-field. A corollary of this result is the tail triviality of strongly Rayleigh processes. This is a generalization of a result due to Lyons which establishes tail triviality for discrete determinantal processes. We also study the tail behavior of negatively associated Gaussian and Gaussian threshold processes. We show that these processes are tail trivial though they do not in general satisfy the summable covariances property. Furthermore, we construct negatively associated Gaussian threshold vectors that are not strongly Rayleigh. This identifies a natural family of negatively associated measures that is not a subset of the class of strongly Rayleigh measures.
