Geodesic
Multifractional brownian fields indexed by metric spaces with distances of negative type
ESAIM: Probability and Statistics, Tome 17 (2013), pp. 219-223

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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.

DOI : 10.1051/ps/2011157
Classification : 60G18, 60G15, 60G52
Keywords: fractional brownian motion, self-similarity, complex variations, H-sssi processes 
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     author = {Istas, Jacques},
     title = {Multifractional brownian fields indexed by metric spaces with distances of negative type},
     journal = {ESAIM: Probability and Statistics},
     pages = {219--223},
     publisher = {EDP-Sciences},
     volume = {17},
     year = {2013},
     doi = {10.1051/ps/2011157},
     mrnumber = {3021316},
     zbl = {1296.60094},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011157/}
}
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Istas, Jacques. Multifractional brownian fields indexed by metric spaces with distances of negative type. ESAIM: Probability and Statistics, Tome 17 (2013), pp. 219-223. doi: 10.1051/ps/2011157

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