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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

Path properties of multifractal Brownian motion


Authors: K. V. Ral’chenko and G. M. Shevchenko
Translated by: N. N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 80 (2009).
Journal: Theor. Probability and Math. Statist. 80 (2010), 119-130
MSC (2000): Primary 60G15, 60G17; Secondary 60G18
Published electronically: August 19, 2010
MathSciNet review: 2541957
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Abstract: A new generalization of fractional Brownian motion (called multifractal Brownian motion) is considered for the case where the Hürst index $ H$ is a function of time $ t$. The pathwise continuity of multifractal Brownian motion is proved. Global and local Hölder properties are also studied.


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Additional Information

K. V. Ral’chenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, Kyiv 01601, Ukraine
Email: k.ralchenko@gmail.com

G. M. Shevchenko
Affiliation: Department of Probability Theory, Statistics and Actuarial Mathematics, Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, Kyiv 01601, Ukraine
Email: zhora@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2010-00799-X
PII: S 0094-9000(2010)00799-X
Keywords: Gaussian process, fractional Brownian motion, multifractal Brownian motion, Hürst index
Received by editor(s): March 12, 2009
Published electronically: August 19, 2010
Additional Notes: The authors are grateful to the European Commission for support of their investigations in the framework of the program “Marie Curie Actions”, grant PIRSES-GA-2008-230804
Article copyright: © Copyright 2010 American Mathematical Society