M相依随机变量的中偏差
发布时间：2018-11-06 08:48
【摘要】：在本文中,我们主要研究M相依随机变量序列,并对其中偏差原理给出了证明。第一章,我们给出了引言,介绍了m相依随机变量序列及其研究背景,大偏差中偏差原理及其研究背景,并简要介绍了我们所要研究的主要的问题。在第二部分,我们给出了我们得到的主要定理,即在改进条件下,M相依随机变量序列的中偏差,并简要叙述了我们在证明主要定理的过程中需要用到的主要引理。第三章,我们将详细给出我们对主要定理和主要引理的证明,证明过程的关键点在于Gartner-Ellis定理的应用,以及对平稳过程定义及性质的熟悉和基本的概率理论等数学基础的掌握。
[Abstract]:In this paper we mainly study the sequence of M-dependent random variables and prove the principle of deviation. In the first chapter, we give the introduction, introduce the sequence of m-dependent random variables and its research background, the principle of large deviation and its research background, and briefly introduce the main problems we want to study. In the second part, we give the main theorems, that is, the intermediate deviation of the sequence of M dependent random variables under the improved condition, and briefly describe the main lemmas we need to use in the process of proving the main theorems. In the third chapter, we will give our proof of the main theorem and the main Lemma in detail. The key point of the proof process is the application of Gartner-Ellis Theorem. Familiarity with the definition and properties of stationary processes and the mastery of the basic mathematical basis such as probability theory.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211
本文编号：2313797
[Abstract]:In this paper we mainly study the sequence of M-dependent random variables and prove the principle of deviation. In the first chapter, we give the introduction, introduce the sequence of m-dependent random variables and its research background, the principle of large deviation and its research background, and briefly introduce the main problems we want to study. In the second part, we give the main theorems, that is, the intermediate deviation of the sequence of M dependent random variables under the improved condition, and briefly describe the main lemmas we need to use in the process of proving the main theorems. In the third chapter, we will give our proof of the main theorem and the main Lemma in detail. The key point of the proof process is the application of Gartner-Ellis Theorem. Familiarity with the definition and properties of stationary processes and the mastery of the basic mathematical basis such as probability theory.
【学位授予单位】：河南师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211
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