Geodesic
Manifold indexed fractional fields
ESAIM: Probability and Statistics, Tome 16 (2012), pp. 222-276

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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.

DOI : 10.1051/ps/2011106
Classification : 60G07, 60G15, 60G18
Keywords: self-similarity, stochastic fields, manifold 
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     author = {Istas, Jacques},
     title = {Manifold indexed fractional fields},
     journal = {ESAIM: Probability and Statistics},
     pages = {222--276},
     publisher = {EDP-Sciences},
     volume = {16},
     year = {2012},
     doi = {10.1051/ps/2011106},
     mrnumber = {2956575},
     zbl = {1275.60041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/ps/2011106/}
}
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Istas, Jacques. Manifold indexed fractional fields. ESAIM: Probability and Statistics, Tome 16 (2012), pp. 222-276. doi: 10.1051/ps/2011106

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