Inequalities Related to Mixing Sequences

Zhengyan Lin () and Zhidong Bai ()
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Zhengyan Lin: Zhejiang University, Department of Mathematics
Zhidong Bai: Northeast Normal University, School of Mathematics and Statistics

Chapter Chapter 10 in Probability Inequalities, 2010, pp 130-148 from Springer

Abstract: Abstract Most theorems in classical probability theory are derived under the assumption of independence of random variables or events. However, in many practical cases, the random variables are dependent. Thus, investigation on dependent random variables has both theoretical and practical importance. In chapter 6, we have introduced the concept of martingales that is a big class of dependent random variables. There is another class of dependent random variables, that is, time-dependent observations or time series. It is imaginable that observations at nearer time instants have stronger dependency while the dependency becomes weaker when the time distance increases. To describe such sequences of random variables, we shall introduce the concept of mixing. There are at least six different definitions of mixing sequences. In this chapter, we only give three most commonly used definitions.

Keywords: Covariance Estimate; Tail Probability; Exponential Estimate; Dependent Random Variable; Classical Probability Theory (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-642-05261-3_10

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