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

DOI:
https://doi.org/10.1090/S0094-9000-2012-00838-7

Published electronically:
February 2, 2012

MathSciNet review:
2768845

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0094-9000-2012-00838-7

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