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Theory of Probability and Mathematical Statistics

ISSN 1547-7363(online) ISSN 0094-9000(print)

 
 

 

Wavelet analysis of a multifractional process in an arbitrary Wiener chaos


Authors: A. Ayache and Y. Esmili
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 98 (2018).
Journal: Theor. Probability and Math. Statist. 98 (2019), 27-49
MSC (2010): Primary 60G17, 60G22
DOI: https://doi.org/10.1090/tpms/1061
Published electronically: August 19, 2019
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Abstract: The well-known multifractional Brownian motion (mBm) is the paradigmatic example of a continuous Gaussian process with non-stationary increments whose local regularity changes from point to point. In this article, using a wavelet approach, we construct a natural extension of mBm which belongs to a homogeneous Wiener chaos of an arbitrary order. Then, we study its global and local behavior.


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Additional Information

A. Ayache
Affiliation: UMR CNRS 8524, Laboratoire Paul Painlevé, Université de Lille, Cité Scientifique, Bâtiment M2, 59655 Villeneuve d’Ascq, France
Email: Antoine.Ayache@univ-lille.fr

Y. Esmili
Affiliation: UMR CNRS 8524, Laboratoire Paul Painlevé, Université de Lille, Cité Scientifique, Bâtiment M2, 59655 Villeneuve d’Ascq, France
Email: Yassine.Esmili@univ-lille.fr

DOI: https://doi.org/10.1090/tpms/1061
Keywords: Wiener chaos, self-similar processes, modulus of continuity, wavelet bases, fractional processes
Received by editor(s): February 8, 2018
Published electronically: August 19, 2019
Additional Notes: The authors are very grateful to the anonymous referee for his valuable comments which have led to improvements of the article. This work has been partially supported by the Labex CEMPI (ANR-11-LABX-0007-01) and the GDR 3475 (Analyse Multifractale).
Article copyright: © Copyright 2019 American Mathematical Society