When does fractional Brownian motion not behave as a continuous function with bounded variation?
Probability
2011-11-11 v2
Abstract
If we compose a smooth function g with fractional Brownian motion B with Hurst index H > 1/2, then the resulting change of variables formula [or It/^o- formula] has the same form as if fractional Brownian motion would be a continuous function with bounded variation. In this note we prove a new integral representation formula for the running maximum of a continuous function with bounded variation. Moreover we show that the analogue to fractional Brownian motion fails.
Cite
@article{arxiv.1004.1071,
title = {When does fractional Brownian motion not behave as a continuous function with bounded variation?},
author = {Ehsan Azmoodeh and Heikki Tikanmäki and Esko Valkeila},
journal= {arXiv preprint arXiv:1004.1071},
year = {2011}
}