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

Chow, Y. S.

Bull. Inst. Math., Acad. Sin. 16, No. 3, 177-201 (1988).

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

Keywords:

rates of convergence; moments; renewal theory