Almost sure central limit theorem for the products of U-statistics

Abstract

Almost sure central limit theorem, U-statistics, Unbounded measurable function,

Almost sure convergence for the maxima of strongly dependent stationary Gaussian vector sequences

“…random variables has been studied by Fahrner and Stadtmüller [6] and Cheng et al [4] respectively. For more related works on ASLT, see [1,[10][11][12][13]. For the weakly dependent stationary Gaussian sequence {X n , n 1} with E X 1 = 0, Var X 1 = 1, Csáki and Gonchigdanzan [5] obtained the ASLT for the maxima if their correlation r n = E X 1 X n+1 satisfies r n log n(log log n) 1+ε = O (1) for some ε > 0.…”