Fourier coefficients of invariant random fields on homogeneous spaces of compact Lie groups

作者：Baldi P^*; Trapani S

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2015, 51(2): 648-671.

DOI：10.1214/14-AIHP600

• Invariant random fields
• Fourier expansions
• Characterization of Gaussian random fields

Let T be a random field invariant under the action of a compact group G. In the line of previous work we investigate properties of the Fourier coefficients as orthogonality and Gaussianity. In particular we give conditions ensuring that independence of the random Fourier coefficients implies Gaussianity. As a consequence, in general, it is not possible to simulate a non-Gaussian invariant random field through its Fourier expansion using independent coefficients.

• 出版日期2015-5