We apply a discrete version of the methodology in \cite{gauss} to obtain a recursive asymptotic expansion for $\esp[h(W)]$ in terms of Poisson expectations, where $W$ is a sum of independent integer-valued random variables and $h$ is a polynomially growing function. We also discuss the remainder estimations.
Discrete versions of the transport equation and the Shepp-Olkin conjecture
Zero bias transformation and asymptotic expansions
Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case
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