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Compound Poisson approximation for nonnegative random variables via Stein’s method. (English) Zbl 0765.60015
The basic aim is to study compound Poisson distribution approximation to sums of independent r.v.’s in the metric of total variation. However, the paper begins with a linear integral equation whose solvability is characterized in terms of compound Poisson measure. The proof uses interesting functional analysis arguments. As examples of application bounds for the error of approximation in the case of local dependence and equiprobable allocations are given.
Reviewer: Z.Jurek (Wrocław)

60E15 Inequalities; stochastic orderings
60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
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