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Zbl 1041.60038
Lacaux, Céline
Real harmonizable multifractional Lévy motions. (English)
[J] Ann. Inst. Henri Poincaré, Probab. Stat. 40, No. 3, 259-277 (2004). ISSN 0246-0203

Summary: The class of real harmonizable multifractional Lévy motions (in short RHMLMs) is introduced. This class is a generalization of the multifractional Brownian motion (in short MBM) and of the class of real harmonizable fractional Lévy motions. One of its main interest is that it contains some non-Gaussian fields which share many properties with the MBM. RHMLMs have locally Hölder sample paths and their Hölder exponent is allowed to vary along the trajectory. Moreover these fields are locally asymptotically self-similar. The multifractional function can be estimated with the localized generalized quadratic variations.

MSC 2000:: *60G17 Sample path properties
62G05 Nonparametric estimation

Keywords: Local asymptotic self-similarity; Multifractional function; Identification

Cited in: Zbl 1224.60080

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