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Manifold indexed fractional fields∗

Published online by Cambridge University Press:  11 July 2012

Jacques Istas
Jacques Istas*
Affiliation:
Laboratoire Jean Kuntzmann, Université de Grenoble et CNRS, 38041 Grenoble Cedex 9, France. Jacques.Istas@imag.fr
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Abstract

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

Keywords

Self-similaritystochastic fieldsmanifold
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 16 , 2012 , pp. 222 - 276
Copyright
© EDP Sciences, SMAI, 2012

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