Bestsennaya, E. V.; Utev, S. A. Supremum of an even moment of sums of independent random variables. (English. Russian original) Zbl 0731.60014 Sib. Math. J. 32, No. 1, 139-141 (1991); translation from Sib. Mat. Zh. 32, No. 1(185), 171-173 (1991). The main result gives the following Theorem: For every integer \(m>1\), \[ \sup E(X_ 1+...+X_ n)^{2m}=\phi^{2m}E(\eta_{\lambda}- \lambda)^{2m}, \] where the supremum is taken over all \(n\geq 1\) and all independent random variables \(X_ 1,X_ 2,...,X_ n\) such that E \(X_ i=0\), \(1\leq i\leq n\), \(E X^ 2_ 1+...+E X^ 2_ n=B,\) and \(E X_ 1^{2m}+...+E X_ n^{2m}=A;\phi =(A/B)^{1/(2m-2)}\), and the random variable \(\eta_{\lambda}\) has Poisson distribution with \(\lambda =(B^ m/A)^{1/(m-1)}\). Reviewer: Z.Rychlik (Lublin) Cited in 1 ReviewCited in 3 Documents MSC: 60E05 Probability distributions: general theory 60G50 Sums of independent random variables; random walks Keywords:sums of independent random variables; Poisson distribution PDFBibTeX XMLCite \textit{E. V. Bestsennaya} and \textit{S. A. Utev}, Sib. Math. J. 32, No. 1, 139--141 (1991; Zbl 0731.60014); translation from Sib. Mat. Zh. 32, No. 1(185), 171--173 (1991) Full Text: DOI References: [1] Yu. V. Prokhorov, ?Extremal problems in limit theorems,? in: Proc. Sixth All-Union Conf. Theory Prob. and Math. Statist. (Vilnius, 1960) [in Russian], Gos. Izd. Polit. i Nauchn. Lit. Litovsk. SSR, Vilnius (1962), pp. 77-84. [2] I. F. Pinelis an S. A. Utev, ?Estimates of moments of sums of independent random variables,? Teor. Veroyatn. Primen.,29, No. 3, 544-547 (1984). [3] S. A. Utev, ?Extremal problems in moment inequalities,? in: Limit Theorems of Probability Theory [in Russian], Tr. Inst. Mat. Sib. Otd., Akad. Nauk SSSR, Novosibirsk (1985). · Zbl 0579.60018 [4] V. P. Leonov and A. N. Shiryaev, ?On a method of calculation of semi-invariants,? Teor. Veroyatn. Primen.,4, No. 3, 342-355 (1959). · Zbl 0087.33701 [5] W. Feller, An Introduction to Probability Theory and Its Applications, Vol. II, Wiley, New York (1966). · Zbl 0138.10207 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.