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Multifractional Brownian fields indexed by metric spaces with distances of negative type

Published online by Cambridge University Press:  08 February 2013

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

We define multifractional Brownian fields indexed by a metric space, such as a manifold with its geodesic distance, when the distance is of negative type. This construction applies when the Brownian field indexed by the metric space exists, in particular for spheres, hyperbolic spaces and real trees.

Type
Research Article
Copyright
© EDP Sciences, SMAI, 2013

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