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- W2056517857 abstract "This paper deals with a Walsh-harmonizable dyadic stationary sequence { X ( k ): k =0, 1, 2,…} which is represented as X(k)= ∫ 0 1 ψ k (λ) dζ(λ) , where ψ k ( λ ) is the k -th Walsh function and ζ ( λ ) is a second-order process with orthogonal increments. One of the aims is to express the process { ζ ( λ ): λ ϵ [0, 1)} in terms of the Walsh–Stieltjes series ∑ X ( k ) ψ k ( λ ) of the original sequence X ( k ). In order to do this a Littlewood's Tauberian theorem for a series of random variables is introduced. A finite Walsh series expression of X ( k ) is derived by introducing an approximate Walsh series of X ( k ). Also derived is a strong law of large numbers for the dyadic stationary sequences." @default.
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- W2056517857 date "1985-07-01" @default.
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- W2056517857 title "Some limit theorems for walsh-harmonizable dyadic stationary sequences" @default.
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- W2056517857 doi "https://doi.org/10.1016/0304-4149(85)90023-7" @default.
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