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