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Poincaré Inequalities and Normal Approximation for Weighted Sums
S. G. Bobkov, G. P. Chistyakov, F. Götze
Under Poincaré-type conditions, upper bounds are explored for the Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. Based on…
Approximation of free convolutions by free infinitely divisible laws
G. P. Chistyakov, F. Götze
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of -fold convolutions of probability measures by free infinitely divisible…
Normal Approximation for Weighted Sums under a Second Order Correlation Condition
S. G. Bobkov, G. P. Chistyakov, F. Götze
Under correlation-type conditions, we derive an upper bound of order for the average Kolmogorov distance between the distributions of weighted sums of dependent summan…
Non-Uniform Bounds in the Poisson Approximation with Applications to Informational Distances. II
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore asymptotically optimal bounds for deviations of distributions of independent Bernoulli random variables from the Poisson limit in terms of the Shannon relative entropy a…
Non-uniform Bounds in the Poisson Approximation with Applications to Informational Distances. I
S. G. Bobkov, G. P. Chistyakov, F. Götze
We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson -distance. Th…
Berry-Esseen Bounds for typical weighted sums
Sergey Bobkov, Gennadiy Chistyakov, Friedrich Götze
Under correlation-type conditions, we derive upper bounds of order for the Kolmogorov distance between the distributions of weighted sums of dependent summands…