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Theory of Probability and Mathematical Statistics

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

   
 
 

 

On the pointwise regularity of the Multifractional Brownian Motion and some extensions


Authors: C. Esser and L. Loosveldt
Journal: Theor. Probability and Math. Statist. 110 (2024), 55-73
MSC (2020): Primary 60G22, 60G17, 26A15, 42C40
DOI: https://doi.org/10.1090/tpms/1206
Published electronically: May 10, 2024
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Abstract: We study the pointwise regularity of the Multifractional Brownian Motion and, in particular, we obtain the existence of so-called slow points of the process, that is points which exhibit a slow oscillation instead of the a.e. regularity. This result entails that a non self-similar process can also exhibit such a behavior. We also consider various extensions with the aim of imposing weaker regularity assumptions on the Hurst function without altering the regularity of the process.


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Additional Information

C. Esser
Affiliation: Université de Liège, Département de mathématique – zone Polytech 1, 12 allée de la Découverte, Bât. B37, B-4000 Liège
Email: celine.esser@uliege.be

L. Loosveldt
Affiliation: Université de Liège, Département de mathématique – zone Polytech 1, 12 allée de la Découverte, Bât. B37, B-4000 Liège
Email: l.loosveldt@uliege.be

Keywords: Multifractional Brownian motion, random wavelets series, modulus of continuity, slow/ordinary/rapid points
Received by editor(s): February 10, 2023
Accepted for publication: July 27, 2023
Published electronically: May 10, 2024
Article copyright: © Copyright 2024 Taras Shevchenko National University of Kyiv