Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres
ESAIM: Probability and Statistics, Volume 16  (2012), p. 165-221

We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.

DOI : https://doi.org/10.1051/ps/2011105
Classification:  60G15,  60G10,  51M10
Keywords: hyperbolic space, random fields, Lévy's brownian field
@article{PS_2012__16__165_0,
     author = {Cohen, S. and Lifshits, M. A.},
     title = {Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {16},
     year = {2012},
     pages = {165-221},
     doi = {10.1051/ps/2011105},
     zbl = {1275.60038},
     mrnumber = {2946126},
     language = {en},
     url = {http://www.numdam.org/item/PS_2012__16__165_0}
}
Cohen, S.; Lifshits, M. A. Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres. ESAIM: Probability and Statistics, Volume 16 (2012) , pp. 165-221. doi : 10.1051/ps/2011105. http://www.numdam.org/item/PS_2012__16__165_0/

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