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- W2968069428 abstract "It is shown that, for any given $pge5$, $A>0$ and $B>0$, the exact upper bound on $mathsf{E}|sum X_i|^p$ over all independent zero-mean random variables (r.v.'s) $X_1,ldots,X_n$ such that $summathsf{E}X_i^2=B$ and $summathsf{E}|X_i|^p=A$ equals $c^pmathsf{E}|Pi_{lambda}-lambda|^p$, where $(lambda ,c)in(0,infty)^2$ is the unique solution to the system of equations $c^plambda=A$ and $c^2lambda=B$, and $Pi_{lambda}$ is a Poisson r.v. with mean $lambda$. In fact, a more general result is obtained, as well as other related ones. As a tool used in the proof, a calculus of variations of moments of infinitely divisible distributions with respect to variations of the Levy characteristics is developed." @default.
- W2968069428 created "2019-08-22" @default.
- W2968069428 creator A5058378725 @default.
- W2968069428 date "2013-04-16" @default.
- W2968069428 modified "2023-09-24" @default.
- W2968069428 title "Exact Rosenthal-type bounds for $pge5$" @default.
- W2968069428 hasPublicationYear "2013" @default.
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