Manifold indexed fractional fields∗
Laboratoire Jean Kuntzmann, Université de Grenoble et
Grenoble Cedex 9,
Revised: 14 April 2010
(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.
Mathematics Subject Classification: 60G07 / 60G15 / 60G18
Key words: Self-similarity / stochastic fields / manifold
© EDP Sciences, SMAI, 2012