Elliptic gaussian random processes.

Albert Benassi; Stéphane Jaffard; Daniel Roux

Revista Matemática Iberoamericana (1997)

  • Volume: 13, Issue: 1, page 19-90
  • ISSN: 0213-2230

Abstract

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We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.

How to cite

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Benassi, Albert, Jaffard, Stéphane, and Roux, Daniel. "Elliptic gaussian random processes.." Revista Matemática Iberoamericana 13.1 (1997): 19-90. <http://eudml.org/doc/39530>.

@article{Benassi1997,
abstract = {We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.},
author = {Benassi, Albert, Jaffard, Stéphane, Roux, Daniel},
journal = {Revista Matemática Iberoamericana},
keywords = {Procesos estocásticos; Operadores pseudodiferenciales; Operadores elípticos; Distribución de Gauss; Ondículas; Movimiento browniano; Gaussian random fields; elliptic pseudo-differential operator; modulus of continuity; multi-fractional Brownian motion},
language = {eng},
number = {1},
pages = {19-90},
title = {Elliptic gaussian random processes.},
url = {http://eudml.org/doc/39530},
volume = {13},
year = {1997},
}

TY - JOUR
AU - Benassi, Albert
AU - Jaffard, Stéphane
AU - Roux, Daniel
TI - Elliptic gaussian random processes.
JO - Revista Matemática Iberoamericana
PY - 1997
VL - 13
IS - 1
SP - 19
EP - 90
AB - We study the Gaussian random fields indexed by Rd whose covariance is defined in all generality as the parametrix of an elliptic pseudo-differential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field in this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the fields in terms of the properties of the principal symbol of the pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.
LA - eng
KW - Procesos estocásticos; Operadores pseudodiferenciales; Operadores elípticos; Distribución de Gauss; Ondículas; Movimiento browniano; Gaussian random fields; elliptic pseudo-differential operator; modulus of continuity; multi-fractional Brownian motion
UR - http://eudml.org/doc/39530
ER -

Citations in EuDML Documents

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  1. Ronan Le Guével, Jacques Lévy Véhel, Incremental moments and Hölder exponents of multifractional multistable processes
  2. Erick Herbin, Benjamin Arras, Geoffroy Barruel, From almost sure local regularity to almost sure Hausdorff dimension for gaussian fields
  3. Serge Cohen, Renaud Marty, Invariance principle, multifractional gaussian processes and long-range dependence
  4. Marianne Clausel, Lacunary Fractional brownian Motion
  5. Hermine Biermé, Frédéric Richard, Estimation of anisotropic gaussian fields through Radon transform
  6. Jacques Istas, Identification des paramètres d'un processus gaussien fractionnaire
  7. Marianne Clausel, Lacunary Fractional Brownian Motion
  8. Céline Lacaux, Real harmonizable multifractional Lévy motions
  9. Hermine Biermé, Frédéric Richard, Estimation of anisotropic Gaussian fields through Radon transform
  10. Yimin Xiao, Properties of local-nondeterminism of Gaussian and stable random fields and their applications

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