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Strong Laws and Summability for Sequences of $phi$-Mixing Random Variables in Banach Spaces

机译:Banach空间中$ phi $ -Mixing随机变量序列的强大定律和可积性

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In this note the almost sure convergence of stationary, $arphi$-mixing sequences of random variables with values in real, separable Banach spaces according to summability methods is linked to the fulfillment of a certain integrability condition generalizing and extending the results for i.i.d. sequences. Furthermore we give via Baum-Katz type results an estimate for the rate of convergence in these laws.
机译:在本说明中,根据求和方法,几乎​​可以肯定地确定了随机变量与实数可分离的Banach空间中具有随机值的静态混合变量序列的收敛性,其与确定和推广i.i.d结果的某些可积性条件的实现有关。序列。此外,我们通过Baum-Katz型结果给出了这些定律的收敛速度的估计。

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