Applications of autoreproducing kernel grammian moduli to (U, H)-valued stationary random functions

B. Truong-Van

Journal of Multivariate Analysis, 1985, vol. 17, issue 1, 56-75

Abstract: It is shown that the analytical characterizations of q-variate interpolable and minimal stationary processes obtained by H. Salehi (Ark. Mat., 7 (1967), 305-311; Ark. Mat., 8 (1968), 1-6; J. Math. Anal. Appl., 25 (1969), 653-662), and later by A. Weron (Studia Math., 49 (1974), 165-183), can be easily extended to Hilbert space valued stationary processes when using the two grammian moduli that respectively autoreproduce their correlation kernel and their spectral measure. Furthermore, for these processes, a Wold-Cramér concordance theorem is obtained that generalizes an earlier result established by H. Salehi and J. K. Scheidt (J. Multivar. Anal., 2 (1972), 307-331) and by A. Makagon and A. Weron (J. Multivar. Anal., 6 (1976), 123-137).

Keywords: Autoreproducing; kernel; grammian; moduli; Hellinger; integrals; Hilbert; space-valued; stationary; process; operator-valued; spectral; measure; interpolability; minimality; Wold-Cramer; concordance; theorem (search for similar items in EconPapers)
Date: 1985
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