Abstract

In this paper, we consider a special class of dependent random variables (APND) that contains negative dependent random variables classes(ND,PND,NUOD,NA,NLOD,) and some classes of positive dependent random variables. Then we generalize Kolmogrov–Feller weak law of large numbers for i.i.d. random variables to APND random variables. we further give corresponding forms of dependence for random elements taking values in separable Banach space. This development will be of use for obtaining Banach space weak law of large numbers.

中文翻译：

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APND 随机变量的 Kolmogrov-Feller 型弱大数定律

摘要

在本文中，我们考虑了一类特殊的因随机变量（APND），它包含负因随机变量类（ND，PND，NUOD，NA，NLOD，）和一些正因随机变量类。然后我们将 iid 随机变量的 Kolmogrov-Feller 大数弱定律推广到 APND 随机变量。我们进一步给出了在可分离 Banach 空间中取值的随机元素的相应依赖形式。这一发展将有助于获得巴拿赫空间弱大数定律。