Multi-dimensional fractional Brownian motion in the G-setting

In this paper we introduce a definition of a multi-dimensional fractional Brownian motion of Hurst index $H\in (0,1)$ under volatility uncertainty (in short G-fBm). We study the properties of such a process and provide first results about stochastic calculus with respect to a fractional G-Brownian motion for a Hurst index $H>\frac{1}{2}$ .