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European Mathematical Society Publishing House
2016-09-19 17:05:43
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
13
1997
1
Elliptic gaussian random processes
Albert
Benassi
Université Blaise Pascal, AUBIÈRE CEDEX, FRANCE
Daniel
Roux
Université Blaise Pascal, AUBIÈRE CEDEX, FRANCE
Stéphane
Jaffard
Université Paris Est, CRÉTEIL CEDEX, FRANCE
We study the Gaussian random fields indexed by $\mathbb R^d$ whose covariance is defi ned in all generality as the parametrix of an elliptic pseudo di fferential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the fi eld on this corresponding basis yields its iterated logarithm law and its uniform modulus of continuity. We also characterize the local scalings of the field in term of the properties of the principal symbol of the pseudodi fferential operator. Similar results are obtained for the Multi- Fractional Brownian Motion .
General
19
90
10.4171/RMI/217
http://www.ems-ph.org/doi/10.4171/RMI/217