Journal of Applied Mathematics and Stochastic Analysis 
Volume 2006 (2006), Article ID 32435, 9 pages
doi:10.1155/JAMSA/2006/32435

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

Abstract

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.