Are fractional Brownian motions predictable?
Probability
2009-07-10 v1
Abstract
We provide a device, called the local predictor, which extends the idea of the predictable compensator. It is shown that a fBm with the Hurst index greater than 1/2 coincides with its local predictor while fBm with the Hurst index smaller than 1/2 does not admit any local predictor. The local predictor of a martingale (in particular: Brownian motion) trivially exists and equals 0.
Cite
@article{arxiv.0907.1618,
title = {Are fractional Brownian motions predictable?},
author = {Adam Jakubowski},
journal= {arXiv preprint arXiv:0907.1618},
year = {2009}
}
Comments
7 pages, to appear in proceedings of the Sixth Seminar on Stochastic Analysis, Random Fields and Applications, Ascona 2008