(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.
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},
pages = {222--276},
year = {2012},
publisher = {EDP Sciences},
volume = {16},
doi = {10.1051/ps/2011106},
mrnumber = {2956575},
zbl = {1275.60041},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2011106/}
}
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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