## 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

### Keywords:

rates of convergence; moments; renewal theory