### MULTIVARIATE RANDOM FIELDS ON SOME HOMOGENEOUS SPACES

**OLEKSANDER PONOMARENKO AND YURIY PERUN**

*Theory of Stochastic Processes*

*Vol.14 (30), no.3-4, 2008, pp.104-113*

The generalized continuous random fields of second order with values in arbitrary complex normed space X in the case when their arguments belong to homogeneous space with compact transformation group G are considered. Such fields are harmonizable in some sense. The spectral representations of homogeneous random fields in X and G-invariant positive definite operator-valued kernels are obtained. The special case of random fields with values in complex Hilbert space and random fields on three-dimensional spheres are also studied.

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