一般的巴赫-埃森不等式及其应用。
General Bahr-Esseen inequalities and their applications.
作者信息
Fazekas István, Pecsora Sándor
机构信息
Faculty of Informatics, University of Debrecen, P.O. Box 400, Debrecen, 4002 Hungary.
出版信息
J Inequal Appl. 2017;2017(1):191. doi: 10.1186/s13660-017-1468-y. Epub 2017 Aug 18.
Abstract
We study the Bahr-Esseen inequality. We show that the Bahr-Esseen inequality holds with exponent if it holds with exponent [Formula: see text] for the truncated and centered random variables. The Bahr-Esseen inequality is also true if the truncated random variables are acceptable. We then apply the results to obtain weak and strong laws of large numbers and complete convergence.
摘要
我们研究巴赫 - 埃森不等式。我们证明，如果对于截断且中心化的随机变量，巴赫 - 埃森不等式以指数[公式：见文本]成立，那么它以指数 也成立。如果截断随机变量是可接受的，巴赫 - 埃森不等式同样成立。然后我们应用这些结果来得到弱大数定律和强大数定律以及完全收敛性。
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