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Theory of Probability and Mathematical Statistics
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
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 79 (2008).
Journal: Theor. Probability and Math. Statist. 79 (2009), 107-116
MSC (2000): Primary 60G15; Secondary 60G44
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

DOI: http://dx.doi.org/10.1090/S0094-9000-09-00773-X
PII: S 0094-9000(09)00773-X
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