Basic properties of the Multivariate Fractional Brownian Motion
Probability
2012-04-27 v2 Statistics Theory
Statistics Theory
Abstract
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm's may be reached as the limit of partial sums of (super)linear processes. Finally, an algorithm to perfectly simulate the mfBm is presented and illustrated by some simulations.
Cite
@article{arxiv.1007.0828,
title = {Basic properties of the Multivariate Fractional Brownian Motion},
author = {Pierre-Olivier Amblard and Jean-François Coeurjolly and Frédéric Lavancier and Anne Philippe},
journal= {arXiv preprint arXiv:1007.0828},
year = {2012}
}
Comments
D\'epartement Images et Signal