Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 32435, 9 pages

On the mixed fractional Brownian motion

Mounir Zili

University Studies Department, Preparatory Institute for Military Academies, Avenue Maréchal Tito, Sousse 4029, Tunisia

Received 3 October 2005; Revised 24 March 2006; Accepted 24 March 2006

Copyright © 2006 Mounir Zili. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The mixed fractional Brownian motion is used in mathematical finance, in the modelling of some arbitrage-free and complete markets. In this paper, we present some stochastic properties and characteristics of this process, and we study the α-differentiability of its sample paths.