Zero bias transformation and asymptotic expansions. (English. French summary) Zbl 1238.60050

Summary: Let \(W\) be a sum of independent random variables. We apply the zero bias transformation to deduce recursive asymptotic expansions for \(\mathbb{E}[h(W)]\) in terms of normal expectations, or of Poisson expectations for integer-valued random variables. We also discuss the estimates of remaining errors.


60G50 Sums of independent random variables; random walks
60F05 Central limit and other weak theorems
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