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April 2004 On roughness indices for fractional fields
Albert Benassi, Serge Cohen, Jacques Istas
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Bernoulli 10(2): 357-373 (April 2004). DOI: 10.3150/bj/1082380223


The class of moving-average fractional Lévy motions (MAFLMs), which are fields parameterized by a d-dimensional space, is introduced. MAFLMs are defined by a moving-average fractional integration of order H of a random Lévy measure with finite moments. MAFLMs are centred d-dimensional motions with stationary increments, and have the same covariance function as fractional Brownian motions. They have H-d/2 Hölder-continuous sample paths. When the Lévy measure is the truncated random stable measure of index α, MAFLMs are locally self-similar with index \widetilde{H} =H -d/2+d/ α. This shows that in a non-Gaussian setting these indices (local self-similarity, variance of the increments, Hölder continuity) may be different. Moreover, we can establish a multiscale behaviour of some of these fields. All the indices of such MAFLMs are identified for the truncated random stable measure.


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Albert Benassi. Serge Cohen. Jacques Istas. "On roughness indices for fractional fields." Bernoulli 10 (2) 357 - 373, April 2004.


Published: April 2004
First available in Project Euclid: 19 April 2004

zbMATH: 1062.60052
MathSciNet: MR2046778
Digital Object Identifier: 10.3150/bj/1082380223

Rights: Copyright © 2004 Bernoulli Society for Mathematical Statistics and Probability


Vol.10 • No. 2 • April 2004
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