Remote Access Theory of Probability and Mathematical Statistics

Theory of Probability and Mathematical Statistics

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

Request Permissions   Purchase Content 
 

 

The distance between fractional Brownian motion and the subspace of martingales with ``similar'' kernels


Authors: V. Doroshenko, Yu. Mishura and O. Banna
Translated by: N. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 87 (2012).
Journal: Theor. Probability and Math. Statist. 87 (2013), 41-49
MSC (2010): Primary 60G15, 60G22; Secondary 60G44
DOI: https://doi.org/10.1090/S0094-9000-2014-00903-5
Published electronically: March 21, 2014
MathSciNet review: 3241445
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the problem of approximation of a fractional Brownian motion with the help of Gaussian martingales that can be represented as the integrals with respect to a Wiener process and with nonrandom integrands being ``similar'' to the kernel of the fractional Brownian motion. The ``similarity'' is understood in the sense that an integrand is the value of the kernel at some point. We establish analytically and evaluate numerically the upper and lower bounds for the distance between the fractional Brownian motion and the space of Gaussian martingales.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Theory of Probability and Mathematical Statistics with MSC (2010): 60G15, 60G22, 60G44

Retrieve articles in all journals with MSC (2010): 60G15, 60G22, 60G44


Additional Information

V. Doroshenko
Affiliation: Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601 Kyiv, Ukraine
Email: vadym.doroshenko@gmail.com

Yu. Mishura
Affiliation: Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601 Kyiv, Ukraine
Email: yumishura@gmail.com

O. Banna
Affiliation: Faculty of Mechanics and Mathematics, Kyiv National Taras Shevchenko University, Volodymyrska 64, 01601 Kyiv, Ukraine

DOI: https://doi.org/10.1090/S0094-9000-2014-00903-5
Keywords: Wiener process, fractional Brownian process, Gaussian martingale, approximation of fractional Brownian motion by Gaussian martingales
Received by editor(s): June 1, 2012
Published electronically: March 21, 2014
Article copyright: © Copyright 2014 American Mathematical Society