Estimates for moments of supremum of reflected fractional Brownian motion

Let $B_H(\cdot)$ be a fractional Brownian motion with Hurst parameter $H\in(0,1]$. Motivated by applications to maximal inequalities for fractional Brownian motion, in this note we derive bounds for K_T(H,\gamma):=E[\sup_{t\in[0,T]}|B_H(t)|]^\gamma, with $\gamma, T>0$.