Revista Matemática Iberoamericana

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Volume 13, Issue 1, 1997, pp. 19–90
DOI: 10.4171/RMI/217

Published online: 1997-04-30

Elliptic gaussian random processes

Albert Benassi[1], Daniel Roux[2] and Stéphane Jaffard[3]

(1) Université Blaise Pascal, Aubière, France
(2) Université Blaise Pascal, Aubière, France
(3) Université Paris Est, Créteil, France

We study the Gaussian random fields indexed by $\mathbb R^d$ whose covariance is defined in all generality as the parametrix of an elliptic pseudodifferential operator with minimal regularity assumption on the symbol. We construct new wavelet bases adapted to these operators; the decomposition of the field 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 pseudodifferential operator. Similar results are obtained for the Multi-Fractional Brownian Motion.

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Benassi Albert, Roux Daniel, Jaffard Stéphane: Elliptic gaussian random processes. Rev. Mat. Iberoam. 13 (1997), 19-90. doi: 10.4171/RMI/217