## 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.

### MSC:

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

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