Some limit theorems for walsh-harmonizable dyadic stationary sequences

Y. Endow

Stochastic Processes and their Applications, 1985, vol. 20, issue 1, 157-167

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.

Keywords: Dyadic; stationary; processes; Walsh-Stieltjes; series; inversion; formula; approximate; Walsh; series; strong; law; of; large; numbers (search for similar items in EconPapers)
Date: 1985
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