A bound for the distance between fractional Brownian motion and the space of Gaussian martingales on an interval
Open Access
- 1 January 2011
- journal article
- Published by American Mathematical Society (AMS) in Theory of Probability and Mathematical Statistics
- Vol. 83, 13-25
- https://doi.org/10.1090/s0094-9000-2012-00838-7
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.Keywords
This publication has 3 references indexed in Scilit:
- Approximation of fractional Brownian motion by Wiener integralsTheory of Probability and Mathematical Statistics, 2009
- Mixed Brownian–fractional Brownian model: absence of arbitrage and related topicsStochastics, 2006
- An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian MotionsBernoulli, 1999