Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres

S. Cohen; M. A. Lifshits

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 165-221
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Cohen, S., and Lifshits, M. A.. "Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres." ESAIM: Probability and Statistics 16 (2012): 165-221. <http://eudml.org/doc/273605>.

@article{Cohen2012,
abstract = {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.},
author = {Cohen, S., Lifshits, M. A.},
journal = {ESAIM: Probability and Statistics},
keywords = {hyperbolic space; random fields; Lévy’s brownian field; Lévy’s Brownian field; Ornstein-Uhlenbeck field; white noise; hyperboloid model; homogeneous fields; horocycles; geodesics; Euclidean sphere},
language = {eng},
pages = {165-221},
publisher = {EDP-Sciences},
title = {Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres},
url = {http://eudml.org/doc/273605},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Cohen, S.
AU - Lifshits, M. A.
TI - Stationary gaussian random fields on hyperbolic spaces and on euclidean spheres
JO - ESAIM: Probability and Statistics
PY - 2012
PB - EDP-Sciences
VL - 16
SP - 165
EP - 221
AB - 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.
LA - eng
KW - hyperbolic space; random fields; Lévy’s brownian field; Lévy’s Brownian field; Ornstein-Uhlenbeck field; white noise; hyperboloid model; homogeneous fields; horocycles; geodesics; Euclidean sphere
UR - http://eudml.org/doc/273605
ER -

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