Moment Estimates of (Maximum of) Sums of Random Variables

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 9 in Probability Inequalities, 2010, pp 97-129 from Springer

Abstract: Abstract Limiting properties of partial sums of a sequence of random variables form one of the largest subjects of probability theory. Therefore, moment estimation of the (maximal) sum of random variables is very important in the research of limiting theorems. In this chapter, we introduce some most important inequalities, such as von Bahr-Esseen, Khintchine, Marcinkiewics-Zygmund-Berkholder inequalities. Proofs of such inequalities are rather involved. Some simpler proofs will be provided in this Chapter. For those with complicated proofs, the references will be given therein.

Keywords: Moment Estimate; Independent Copy; Minkowski Inequality; Elementary Inequality; Important Inequality (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-05261-3_9

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DOI: 10.1007/978-3-642-05261-3_9

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