Interpolation of q-variate weakly stationary stochastic processes over a locally compact abelian group

Habib Salehi and John K. Scheidt

Journal of Multivariate Analysis, 1972, vol. 2, issue 3, 307-331

Abstract: Let G be a discrete locally compact abelian group. Let (xg)g[set membership, variant]G be a q-variate weakly stationary stochastic process indexed by elements g of G. A. N. Kolmogorov, P. Masani, H. Salehi and others have derived numerous results on the minimality and interpolation of random processes indexed by the integers. The main efforts of this work are to derive similar results for multivariate processes indexed by the group G. Although the ideas and concepts used here are similar to the ones used earlier by other authors, some of the techniques are different, since the integers are ordered and singly generated, whereas an arbitrary group need not be. Results such as Kolmogorov's Minimality Theorem, the Wold Decomposition Theorem, the Wold-Cramér Concordance Theorem and several theorems on interpolation of (xg)g[set membership, variant]G are obtained.

Keywords: Locally; compact; abelian; group; Haar; measure; q-variate; weakly; stationary; stochastic; processes; spectral; distribution; minimality; interpolation; Wold; Decomposition; Cramer; Decomposition; Wold-Cramer; Concordance; Theorem; regularity; singularity (search for similar items in EconPapers)
Date: 1972
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(72)90019-X
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:2:y:1972:i:3:p:307-331

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().