Borisov, I. S. Moment inequalities connected with accompanying Poisson laws in Abelian groups. (English) Zbl 1031.60005 Int. J. Math. Math. Sci. 2003, No. 44, 2771-2786 (2003). Let \(X_i\) be independent random variables with respective distributions \(P_i\) taking values in a measurable Abelian group \(G\), \(S_n=X_1+\cdots +X_n\). The author obtains exact moment inequalities for some measurable functions of \(S_n\) via the analogous moments of the accompanying Poisson law, the generalized Poisson distribution with the Lévy measure \(\mu =P_1+\cdots +P_n\). The case where \(G\) is a Banach space is considered in detail. As an application, estimates of the expectation of some functionals of empirical processes are given. Reviewer: Anatoly N.Kochubei (Kyïv) Cited in 4 Documents MSC: 60B15 Probability measures on groups or semigroups, Fourier transforms, factorization 60B11 Probability theory on linear topological spaces 60E15 Inequalities; stochastic orderings Keywords:independent random variables; accompanying Poisson law; empirical process PDFBibTeX XMLCite \textit{I. S. Borisov}, Int. J. Math. Math. Sci. 2003, No. 44, 2771--2786 (2003; Zbl 1031.60005) Full Text: DOI EuDML