On spectral representations of tensor random fields on the sphere

Details On spectral representations of tensor random fields on the sphere On spectral representations of tensor random fields on the sphere

2009-12-17

arxiv.org/abs/0912.3389v1

Stochastic Analysis and Applications, Vol. 30 (2012), 44-66

Mathematics

Probability

21 pages

Scientific paper

We study the representations of tensor random fields on the sphere basing on the theory of representations of the rotation group. Introducing specific components of a tensor field and imposing the conditions of weak isotropy and mean square continuity, we derive their spectral decompositions in terms of generalized spherical functions. The properties of random coefficients of the decompositions are characterized, including such an important question as conditions of Gaussianity.

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