A supplement to the complete convergence

Liu Weidong and Lin Zhengyan

Statistics & Probability Letters, 2006, vol. 76, issue 7, 748-754

Abstract: Let X,X1,X2,... be independent identically distributed random variables. Then, Baum and Katz [1965. Convergence rates in the law of large numbers. Trans. Amer. Math. Soc. 120, 108-123] proved that for p>1,if and only if and . We prove thatif and only if and is slowly varying as x-->[infinity].

Keywords: Complete; convergence; Independent; random; variable; Slowly; varying; function (search for similar items in EconPapers)
Date: 2006
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