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Fine regularity of Lévy processes and linear (multi)fractional stable motion


 
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1. Title Title of document Fine regularity of Lévy processes and linear (multi)fractional stable motion
 
2. Creator Author's name, affiliation, country Paul Balança; École Centrale Paris; France
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) 2-microlocal analysis; Hölder regularity; multifractal spectrum; oscillating singularities; Lévy processes; linear fractional stable motion
 
3. Subject Subject classification 60G07; 60G17; 60G22; 60G44
 
4. Description Abstract In this work, we investigate the fine regularity of Lévy processes using the 2-microlocal formalism. This framework allows us to refine the multifractal spectrum determined by Jaffard and, in addition, study the oscillating singularities of Lévy processes. The fractal structure of the latter is proved to be more complex than the classic multifractal spectrum and is determined in the case of alpha-stable processes. As a consequence of these fine results and the properties of the 2-microlocal frontier, we are also able to completely characterise the multifractal nature of the linear fractional stable motion (extension of fractional Brownian motion to α-stable measures) in the case of continuous and unbounded sample paths as well. The regularity of its multifractional extension is also presented, indirectly providing an example of a stochastic process with a non-homogeneous and random multifractal spectrum.
 
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7. Date (YYYY-MM-DD) 2014-10-26
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/3393
 
10. Identifier Digital Object Identifier 10.1214/EJP.v19-3393
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 19
 
12. Language English=en en
 
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