Non-Uniform Bounds in the Poisson Approximation With Applications to Informational Distances I

We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson <inline-formula> <tex-math notation="LaTeX">$\chi ^{2}$ </tex-math></inline-formula>-distance. The results are based on proper non-uniform estimates for densities. This part deals with the so-called non-degenerate case.

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