Displaying similar documents to “Manifold indexed fractional fields∗”

Manifold indexed fractional fields

Jacques Istas (2012)

ESAIM: Probability and Statistics

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(Local) self-similarity is a seminal concept, especially for Euclidean random fields. We study in this paper the extension of these notions to manifold indexed fields. We give conditions on the (local) self-similarity index that ensure the existence of fractional fields. Moreover, we explain how to identify the self-similar index. We describe a way of simulating Gaussian fractional fields.

Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres

S. Cohen, M. A. Lifshits (2012)

ESAIM: Probability and Statistics

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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.