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

Author

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  • Salehi, Habib
  • Scheidt, John K.

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.

Suggested Citation

  • Salehi, Habib & Scheidt, John K., 1972. "Interpolation of q-variate weakly stationary stochastic processes over a locally compact abelian group," Journal of Multivariate Analysis, Elsevier, vol. 2(3), pages 307-331, September.
    • Handle: RePEc:eee:jmvana:v:2:y:1972:i:3:p:307-331
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    Cited by:

    1. Bansal, Naveen & Hamedani, G. G. & Zhang, Hao, 2000. "A note on random fields forming conditional bases," Statistics & Probability Letters, Elsevier, vol. 50(4), pages 397-400, December.

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