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Multidimensional covariant random fields on commutative locally compact groups

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Abstract

Homogeneous in the wide sense, covariant random fields on commutative local compact groups with values in finite-dimensional complex Hilbert spaces are considered. The general formula for the correlation operator of such a field is proved, as well as the spectral representation of the field itself in the form of a series of stochastic integrals with respect to orthogonal random measures.

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Authors and Affiliations

  1. Kiev University, USSR

    A. A. Mal'yarenko & A. Ya. Olenko

Authors
  1. A. A. Mal'yarenko
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  2. A. Ya. Olenko
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 11, pp. 1505–1510, November, 1992.

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Mal'yarenko, A.A., Olenko, A.Y. Multidimensional covariant random fields on commutative locally compact groups. Ukr Math J 44, 1384–1389 (1992). https://doi.org/10.1007/BF01071512

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  • DOI: https://doi.org/10.1007/BF01071512

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