Manifold indexed fractional fields
ESAIM: Probability and Statistics, Volume 16  (2012), p. 222-276

(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 : https://doi.org/10.1051/ps/2011106
Classification:  60G07,  60G15,  60G18
Keywords: self-similarity, stochastic fields, manifold
@article{PS_2012__16__222_0,
     author = {Istas, Jacques},
     title = {Manifold indexed fractional fields},
     journal = {ESAIM: Probability and Statistics},
     publisher = {EDP-Sciences},
     volume = {16},
     year = {2012},
     pages = {222-276},
     doi = {10.1051/ps/2011106},
     zbl = {1275.60041},
     mrnumber = {2956575},
     language = {en},
     url = {http://www.numdam.org/item/PS_2012__16__222_0}
}
Istas, Jacques. Manifold indexed fractional fields. ESAIM: Probability and Statistics, Volume 16 (2012) , pp. 222-276. doi : 10.1051/ps/2011106. http://www.numdam.org/item/PS_2012__16__222_0/

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