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

A bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval


Authors: O. L. Banna and Yu. S. Mishura
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 83 (2010).
Journal: Theor. Probability and Math. Statist. 83 (2011), 13-25
MSC (2010): Primary 60G15; Secondary 60G44
Published electronically: February 2, 2012
MathSciNet review: 2768845
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Abstract: We obtain a lower bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval. The distances between fractional Brownian motion and some subspaces of Gaussian martingales are compared. The upper and lower bounds are obtained for the constant in the representation of a fractional Brownian motion in terms of the Wiener process.


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Additional Information

O. L. Banna
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: bannaya@mail.univ.kiev.ua

Yu. S. Mishura
Affiliation: Department of Probability Theory, Statistics, and Actuarial Mathematics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue 2, Kiev 03127, Ukraine
Email: myus@univ.kiev.ua

DOI: http://dx.doi.org/10.1090/S0094-9000-2012-00838-7
PII: S 0094-9000(2012)00838-7
Keywords: Wiener process, fractional Brownian motion, Gaussian martingale, approximation in a class of functions
Received by editor(s): April 7, 2010
Published electronically: February 2, 2012
Article copyright: © Copyright 2012 American Mathematical Society