Manifold indexed fractional fields

Jacques Istas

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 222-276
  • ISSN: 1292-8100


(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.

How to cite


Istas, Jacques. "Manifold indexed fractional fields." ESAIM: Probability and Statistics 16 (2012): 222-276. <>.

abstract = {(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.},
author = {Istas, Jacques},
journal = {ESAIM: Probability and Statistics},
keywords = {self-similarity; stochastic fields; manifold; Gaussian field; stable field; Euclidean random field},
language = {eng},
pages = {222-276},
publisher = {EDP-Sciences},
title = {Manifold indexed fractional fields},
url = {},
volume = {16},
year = {2012},

AU - Istas, Jacques
TI - Manifold indexed fractional fields
JO - ESAIM: Probability and Statistics
PY - 2012
PB - EDP-Sciences
VL - 16
SP - 222
EP - 276
AB - (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.
LA - eng
KW - self-similarity; stochastic fields; manifold; Gaussian field; stable field; Euclidean random field
UR -
ER -


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