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Moment Estimates of (Maximum of) Sums of Random Variables

In: Probability Inequalities

Author

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  • Zhengyan Lin

    (Zhejiang University, Department of Mathematics)

  • Zhidong Bai

    (Northeast Normal University, School of Mathematics and Statistics
    National University of Singapore, Department of Statistics and Applied Probabilty)

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.

Suggested Citation

  • Zhengyan Lin & Zhidong Bai, 2010. "Moment Estimates of (Maximum of) Sums of Random Variables," Springer Books, in: Probability Inequalities, chapter 0, pages 97-129, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-05261-3_9
    DOI: 10.1007/978-3-642-05261-3_9
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