Resumen de Exact Rosenthal-type bounds
It is shown that, for any given p≥5, A>0 and B>0, the exact upper bound on E|∑Xi|p over all independent zero-mean random variables (r.v.’s) X1,…,Xn such that ∑EX2i=B and ∑E|Xi|p=A equals cpE|Πλ−λ|p, where (λ,c)∈(0,∞)2 is the unique solution to the system of equations cpλ=A and c2λ=B, and Πλ is a Poisson r.v. with mean λ. 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 Lévy characteristics is developed.
