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Some limit theorems for walsh-harmonizable dyadic stationary sequences

Author

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  • Endow, Y.

Abstract

This paper deals with a Walsh-harmonizable dyadic stationary sequence {X(k): k=0, 1, 2,...} which is represented as , where [psi]k([lambda]) is the k-th Walsh function and [zeta]([lambda]) is a second-order process with orthogonal increments. One of the aims is to express the process {[zeta]([lambda]): [lambda] [epsilon][0, 1)} in terms of the Walsh-Stieltjes series [summation operator] X(k)[psi]k([lambda]) 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.

Suggested Citation

  • Endow, Y., 1985. "Some limit theorems for walsh-harmonizable dyadic stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 20(1), pages 157-167, July.
    • Handle: RePEc:eee:spapps:v:20:y:1985:i:1:p:157-167
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