用指定的混合系数构造过程
Constructing processes with prescribed mixing coefficients
摘要：
在随机过程中，未来和过去观测之间的依赖性衰减的速率可以用混合系数来量化。后者又出现在强大数定律和相关随机变量的测量结果的集中。自20世纪60年代以来，关于各种混合概念的可能速率的问题已经提出，并且对强混合条件理论中的一些开放问题具有重要意义。本文讨论了$η$ -混合，一个在[Kontorovich和Ramanan]中定义的概念，它与$ϕ$ -混合密切相关。我们表明，存在措施的有限序列基本上是任意的$η$混合系数，以及任意慢混合速率的过程。
英文摘要：
The rate at which dependencies between future and past observations decay in a random process may be quantified in terms of mixing coefficients. The latter in turn appear in strong laws of large numbers and concentration of measure results for dependent random variables. Questions regarding what rates are possible for various notions of mixing have been posed since the 1960's, and have important implications for some open problems in the theory of strong mixing conditions. This paper deals with $η$-mixing, a notion defined in [Kontorovich and Ramanan], which is closely related to $ϕ$-mixing. We show that there exist measures on finite sequences with essentially arbitrary $η$-mixing coefficients, as well as processes with arbitrarily slow mixing rates.
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