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Contents of PMS, Vol. 22, Fasc. 1,
pages 155 - 165
 

THE MAXIMAL J -REGULAR PART OF A q -VARIATE WEAKLY STATIONARY PROCESS

Lutz Klotz

Abstract: Let x be a q -variate (weakly) stationary process over a locally compact Abelian group G , and J a family of subsets of G invariant under translation. We show that the set of all regular non-negative Hermitian matrix-valued measures M not exceeding the (non-stochastic) spectral measure of x and such that the Hilbert space L2(M ) is J -regular contains a unique maximal element. Moreover, this maximal element coincides with the spectral measure of the J -regular part of the Wold decomposition of x.

1991 AMS Mathematics Subject Classification: Primary 60G25; Secondary 15A57.

Key words and phrases: -

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