Abstract
The almost sure invariance principle for some degenerate U-statistics of degree two is considered for strictly stationary random variables satisfying mixing conditions. The error term obtained is O( t 1 − γ ) which yields Donsker's and Strassen's invariance principles for the U-statistics. The approach used here is based upon Hoeffding's expansion of kernel functions and the almost sure invariance principles for partial sums of Banach space valued mixing random variables.
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