- 期刊
ON THE ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENTS IN D[0,1]
並列摘要
Let {w_n} be a sequence of positive constants and W_n = w_l+...+ w_n where W_n →∞ and w_n/W_n →∞. Let {W_n} be a sequence of independent random elements in D[0,1]. The almost sure convergence of W_n^(-1) Σ_(k=1)^n w_k X_k is established under certain integral conditions and growth conditions on the weights {w_n}. The results are shown to be substantially stronger than the weighted sums convergence results of Taylor and Daffer (1980) and the strong laws of large numbers of Ranga Rao (1963) and Daffer and Taylor (1979).
延伸閱讀
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