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On the rate of moment convergence of sample sums and extremes. (English) Zbl 0655.60028

Let \(X_ 1\), \(X_ 2\),... be independent, identically distributed random variables, let \(S_ n\) be their partial sums, \(S^*_ n=\max_{j\leq n}| S_ j|\) and \(X^*_ n=\max_{j\leq n}| X_ j|\). The author investigates rates of convergence for the moments of \(S^*_ n\) and \(X^*_ n\) and for moments of these quantities when they are randomly indexed. Applications, for example, to renewal theory are given.
Reviewer: A.Gut

MSC:

60F25 \(L^p\)-limit theorems
60F10 Large deviations
60G50 Sums of independent random variables; random walks
60K15 Markov renewal processes, semi-Markov processes
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