On the almost sure convergence of weighted sums of random elements in D [0,1]

R. L. Taylor and C. A. Calhoun

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-8

Abstract:

Let { w n } be a sequence of positive constants and W n = w 1 + … + 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 ∑ 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).

Date: 1981
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:131697

DOI: 10.1155/S0161171281000574

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