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Creators/Authors contains: "Chistyakov, G. P."

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  1. ; ; (, Electronic Journal of Probability)
    We explore probability distributions on the real line whose Laplace transform admits an upper bound of subgaussian type known as strict subgaussianity. One class in this family corresponds to entire characteristic functions having only real zeros in the complex plane. Using Hadamard’s factorization theorem, we extend this class and propose new sufficient conditions for strict subgaussianity in terms of location of zeros of the associated characteristic functions. The second part of this note deals with Laplace transforms of strictly subgaussian distributions with periodic components. This class contains interesting examples, for which the central limit theorem with respect to the Rényi entropy divergence of infinite order holds. 
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  2. ; ; (, Electronic journal of probability)
    null (Ed.)
    Under Poincare-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 improved concentration inequalities on high-dimensional Euclidean spheres, the results extend and refine previous results to non-symmetric models. 
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  3. ; ; (, The Annals of probability)
    null (Ed.)
    Under correlation-type conditions, we derive an upper bound of order (log n)/n for the average Kolmogorov distance between the distributions of weighted sums of dependent summands and the normal law. The result is based on improved concentration inequalities on high-dimensional Euclidean spheres. Applications are illustrated on the example of log-concave probability measures. 
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  4. ; ; (, Lithuanian mathematical journal)
    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 and Rényi/relative Tsallis distances (including Pearson’s χ2). This part generalizes the results obtained in Part I and removes any constraints on the parameters of the Bernoulli distributions. 
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    Accepted Manuscript Full Text Available
  5. ; ; (, IEEE transactions on information theory)
    We explore asymptotically optimal bounds for deviations of Bernoulli convolutions from the Poisson limit in terms of the Shannon relative entropy and the Pearson chi-squared 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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    Accepted Manuscript Full Text Available