Large deviations for subordinated fractional Brownian motion and applications

Let WH={WH(t),t∈R} be a real valued fractional Brownian motion with Hurst index H∈(0,1) and let T={Tt,t≥0} be an inverse α-stable subordinator independent of WH. The inverse stable subordinator fractional Brownian motion ZH={ZH(t),t≥0} is defined by ZH(t)=WH(Tt), which may arise as scaling limit of CTRW or random walk in a random environment. In this paper we establish large deviation results for the process ZH and its supremum process. And we also give asymptotic properties of the tail probability of the supremum process.