Almost sure invariance principles for mixing sequences of random variables

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Abstract

An almost sure invariance principle for stationary mixing sequences of random variables with mean zero and finite variance is obtained when the mixing rate satisfies Σnø12(2n) < ∞ or ρ(n)= O(logr n) for some r > 1. A similar result is also given under a higher moment condition.

MSC

Primary 60F17
Secondary 60F15

Keywords

ø-mixing
ρ-mixing
partial sums
almost sure invariance principle
law of the iterated logarithm

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Research supported by the Fok Yingtung Education Foundation, and by National Natural Science Foundation of China.