Zobrazeno 1 - 10
of 16
pro vyhledávání: '"60E, 60F"'
Autor:
Bobkov, Sergey, Götze, Friedrich
Berry-Esseen-type bounds are developed in the multidimensional local limit theorem in terms of the Lyapunov coefficients and maxima of involved densities.
Externí odkaz:
http://arxiv.org/abs/2407.20744
Autor:
Bobkov, Sergey, Götze, Friedrich
The paper is devoted to the investigation of Esscher's transform on high dimensional Euclidean spaces in the light of its application to the central limit theorem. With this tool, we explore necessary and sufficient conditions of normal approximation
Externí odkaz:
http://arxiv.org/abs/2407.20726
Autor:
Bobkov, Sergey G., Götze, Friedrich
For normalized sums $Z_n$ of i.i.d. random variables, we explore necessary and sufficient conditions which guarantee the normal approximation with respect to the R\'enyi divergence of infinite order. In terms of densities $p_n$ of $Z_n$, this is a st
Externí odkaz:
http://arxiv.org/abs/2402.02259
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
Publikováno v:
Lith Math J, 63, 138 - 160, 2023
We give a detailed exposition of the proof of Richter's local limit theorem in a refined form, and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing). We also d
Externí odkaz:
http://arxiv.org/abs/2208.09534
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
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
Autor:
Bobkov, Sergey, Roberto, Cyril
We discuss optimal bounds on the Rényi entropies in terms of the Fisher information. In Information Theory, such relations are also known as entropic isoperimetric inequalities.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=od_____10055::8267d9377c10362427f2ab31baa0dadf
https://hal.science/hal-03825889/file/Entropic.isoperimetric.inequalities.pdf
https://hal.science/hal-03825889/file/Entropic.isoperimetric.inequalities.pdf