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- W2031871185 abstract "Abstract Given a triangular array a = { a n , k , 1 ⩽ k ⩽ k n , n ⩾ 1 } of positive reals, we study the complete convergence property of T n = ∑ k = 1 k n a n , k X n , k for triangular arrays X = { X n , k , 1 ⩽ k ⩽ k n , n ⩾ 1 } of independent random variables. In the Gaussian case we obtain a simple characterization of density type. Using Skorohod representation and Gaussian randomization, we then derive sufficient criteria for the case when X n , k are in L p , and establish a link between the L p -case and L 2 p -case in terms of densities. We finally obtain a density type condition in the case of uniformly bounded random variables." @default.
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- W2031871185 date "2007-06-01" @default.
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- W2031871185 title "On complete convergence of triangular arrays of independent random variables" @default.
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- W2031871185 doi "https://doi.org/10.1016/j.spl.2006.12.011" @default.
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