Convergence of weighted sums of random elements in D[0, 1] |
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| Authors: | Robert Lee Taylor Peter Z Daffer |
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| Institution: | Department of Mathematics, Computer Science & Statistics, University of South Carolina, Columbia, South Carolina, USA;Department of Mathematics & Statistics, Louisiana Tech University, Ruston, Louisiana, USA |
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| Abstract: | Convergence in probability for Toeplitz weighted sums is obtained for convex tight random elements in D0, 1] under pointwise conditions. The almost sure convergence of the weighted sums is proved for independent, convex tight random elements and for independent, identically distributed random elements. Special techniques and concepts are developed in order to obtain these results in the Skorohod topology of D0, 1]. |
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| Keywords: | 60B10 convergence in probability weighted sums Skorohod topology |
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