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Theory of Probability and Mathematical Statistics

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

 
 

 

Approximation of fractional Brownian motion by Wiener integrals


Authors: Yu. S. Mishura and O. L. Banna
Translated by: Oleg Klesov
Journal: Theor. Probability and Math. Statist. 79 (2009), 107-116
MSC (2000): Primary 60G15; Secondary 60G44
DOI: https://doi.org/10.1090/S0094-9000-09-00773-X
Published electronically: December 28, 2009
MathSciNet review: 2494540
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Abstract: We find an approximation in the space $L_\infty ([0,T];L_2(\Omega ))$ of a fractional Brownian motion by martingales of the form $\int _0^ta(s) dW_s$, where $W$ is a Wiener process, $a(s)$ is a power function with a negative index, that is $a(s)=k\cdot s^{-\alpha }$ where $k>0$, $\alpha =H-1/2$, and $H$ is the index of fractional Brownian motion.


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Additional Information

Yu. S. Mishura
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: myus@univ.kiev.ua

O. L. Banna
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 6, Kyiv 03127, Ukraine
Email: bannaya@mail.univ.kiev.ua

Keywords: Wiener integral, fractional Brownian motion
Received by editor(s): September 17, 2007
Published electronically: December 28, 2009
Article copyright: © Copyright 2009 American Mathematical Society