Geodesic
On ergodicity of Gaussian homogeneous random fields on homogeneous spaces
Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 177-180

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A class of homogeneous spaces is found on which all Gaussian homogeneous fields without constant random component are ergodic. In particular, the Minkovsky space and Lobachevsky space belong to this class. 
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     author = {A. A. Tempel'man},
     title = {On ergodicity of {Gaussian} homogeneous random fields on homogeneous spaces},
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     year = {1973},
     language = {ru},
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A. A. Tempel'man. On ergodicity of Gaussian homogeneous random fields on homogeneous spaces. Teoriâ veroâtnostej i ee primeneniâ, Tome 18 (1973) no. 1, pp. 177-180. http://geodesic.mathdoc.fr/item/TVP_1973_18_1_a15/