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On moments of ladder height variables. (English) Zbl 0598.60079
Let \(X_ 1,X_ 2,...,X_ n,..\). be i.i.d. random variables. Define \(S_ 0=0\), \(S_ n=X_ 1+...+X_ n\), \(N=\inf \{n\geq 1:\) \(S_ n\leq 0\}\). The author gives necessary and sufficient conditions in order that \(E| S_ N|^ p<\infty\) for \(p\geq 1\). He points out some problems. In particular, what is the necessary and sufficient condition for \(E| S_ N|^ p<\infty\) when \(0<p<1\).
Reviewer: V.M.Kruglov

MSC:
60G50 Sums of independent random variables; random walks
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