Asymptotic Theory of Weakly Dependent Random Processes
Asymptotic Theory of Weakly Dependent Random Processes
复制标题
DOI：
10.1007/978-3-662-54323-8
复制
发表时间：
2017-05
期刊：
影响因子：
--
通讯作者：
E. Rio
中科院分区：
文献类型：
--
作者：
E. Rio
这些讲义是《Théorie asymptotique des processus aléatoires faiblement dépendants》一书的第二个版本，用法语编写。在翻译过程中，删除了一些印刷错误和不准确之处，更详细地重写了一些校样，添加了一些最近的参考文献，并纳入了三个新部分。然而，初始部分的编号保持不变。下面我对这三个新的部分进行点评。 1.7 节给出了强混合序列的另一个协方差不等式。这个协方差不等式是作者在1991年底得到的练习8的不等式（7）的改进。4.4节讨论了三角形数组的中心极限定理。本节基于作者关于 Lindeberg 方法的论文。昆虫。 5.6 陈述并证明了无界随机变量的有意义的 Peligrad 耦合引理。最初版本的数学工作于 1999 年 1 月完成。从那时起，出现了大量新结果。特别是，现在很明显，本书中使用的弱依赖概念对于某些应用来说限制性太大，例如与某些动态系统相关的马尔可夫链的情况。因此，引入了一些新的弱依赖概念。我们参考 Dedecker 等人（2007）对这些新的依赖性概念及其相关的依赖性系数的介绍，以及这些新技术的一些应用。在第二版中，我们不会处理这种更广泛的依赖关系。最后，我们很高兴感谢 Marina Reizakis 以及 Springer 为本书的制作做出贡献的所有员工。
These lecture notes are the second version of the book “Théorie asymptotique des processus aléatoires faiblement dépendants”, written in French. In the process of translation, some misprints and inaccuracies have been removed, some proofs rewritten in more detail, some recent references have been added and three new sections incorporated. However, the numeration of the initial sections remains unchanged. Below I give comments on the three newsections. Section 1.7 gives another covariance inequality for strongly mixing sequences. This covariance inequality is an improvement of Inequality (7) of Exercise 8, obtained by the author at the end of 1991. Section 4.4 deals with the central limit theorem for triangular arrays. This section is based on a paper of the author on the Lindeberg method. In Sect. 5.6 a meaningful coupling lemma of Peligrad for unbounded random variables is stated and proved. The mathematics of the initial version was completed in January 1999. Since that time, there has been a huge amount of new results. In particular, it is now clear that the notions of weak dependence used in this book are too restrictive for some applications, for instance in the case of Markov chains associated to some dynamical systems. Consequently some new notions of weak dependence have been introduced. We refer to Dedecker et al.(2007) for an introduction to these new notions of dependence and their associated coefficients of dependence, as well as some applications of these new techniques. We will not treat this much broader spectrum of dependence in this second edition. Finally, it is a pleasure to thank Marina Reizakis and all the staff at Springer who contributed towards the production of this book.