Zobrazeno 1 - 10
of 103
pro vyhledávání: '"Chistyakov, G. P."'
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables whose joint
Externí odkaz:
http://arxiv.org/abs/2308.02693
We explore the class of probability distributions on the real line whose Laplace transform admits a strong upper bound of subgaussian type. Using Hadamard's factorization theorem, we extend the class $\mathfrak L$ of Newman and propose new sufficient
Externí odkaz:
http://arxiv.org/abs/2308.01749
Under Poincar\'e-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 sp
Externí odkaz:
http://arxiv.org/abs/2011.09237
Autor:
Chistyakov, G. P., Götze, F.
Based on the~method of subordinating functions we prove bounds for the minimal error of approximations of $n$-fold convolutions of probability measures by free infinitely divisible probability measures.
Externí odkaz:
http://arxiv.org/abs/2010.06516
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 R\'enyi/Tsallis relative distances (including Pearson's $\chi^2$).
Externí odkaz:
http://arxiv.org/abs/1906.09156
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 i
Externí odkaz:
http://arxiv.org/abs/1906.09063
Akademický článek
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Publikováno v:
The Annals of Probability, 2020 May 01. 48(3), 1202-1219.
Externí odkaz:
https://www.jstor.org/stable/26922946
We explore properties of the $\chi^2$ and more general R\'enyi (Tsallis) distances to the normal law. In particular we provide necessary and sufficient conditions for the convergence to the normal law in the central limit theorem using these distance
Externí odkaz:
http://arxiv.org/abs/1608.01805
Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer's theorem with respect to relative entropy and Fisher information distance.
Externí odkaz:
http://arxiv.org/abs/1512.03571