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Strong laws and summability for sequences of \(\varphi\)-mixing random variables in Banach spaces. (English) Zbl 0890.60026
Summary: The almost sure convergence of stationary, \(\varphi\)-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.

MSC:
60F15 Strong limit theorems
40G05 Cesàro, Euler, Nörlund and Hausdorff methods
40G10 Abel, Borel and power series methods
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