On the sub-mixed fractional Brownian motion

Abstract

Let $S_t^H,t\ge 0$ be a linear combination of a Brownian motion and of an independent sub-fractional Brownian motion with Hurst index $0<H<1$. Its main properties are studied and it is shown that $S^H$ can be considered as an intermediate process between a sub-fractional Brownian motion and a mixed fractional Brownian motion. Finally, we determine the values of $H$ for which $S^H$ is not a semi-martingale.

27 pages