Images of fractional Brownian motion with deterministic drift: Positive Lebesgue measure and non-empty interior
Images of fractional Brownian motion with deterministic drift: Positive Lebesgue measure and non-empty interior
Abstract Let $B^{H}$ be a fractional Brownian motion in $\mathbb{R}^{d}$ of Hurst index $H\in\left(0,1\right)$ , $f\;:\;\left[0,1\right]\longrightarrow\mathbb{R}^{d}$ a Borel function and $A\subset\left[0,1\right]$ a Borel set. We provide sufficient conditions for the image $(B^{H}+f)(A)$ to have a positive Lebesgue measure or to have a non-empty interior. This is done through the study …