Mixed Sub-Fractional Brownian Motion
Probability
2013-12-13 v1
Abstract
A new extension of the sub-fractional Brownian motion, and thus of the Brownian motion, is introduced. It is a linear combination of a finite number of sub-fractional Brownian motions, that we have chosen to call the mixed sub-fractional Brownian motion. In this paper, we study some basic properties of this process, its non-Markovian and non-stationarity characteristics, the conditions under which it is a semimartingale, and the main features of its sample paths. We also show that this process could serve to get a good model of certain phenomena, taking not only the sign (like in the case of the sub-fractional Brownian motion), but also the strength of dependence between the increments of this phenomena into account.
Cite
@article{arxiv.1312.3546,
title = {Mixed Sub-Fractional Brownian Motion},
author = {Mounir Zili},
journal= {arXiv preprint arXiv:1312.3546},
year = {2013}
}