Large deviations for subordinated Brownian motion and applications

This paper concerns the problem of large deviation for the subordinated process ZH(t)=WH(T(t))ZH(t)=WH(T(t)). The process WH={WH(t),t∈R}WH={WH(t),t∈R} is the fractional Brownian motion with Hurst index H∈(0,1)H∈(0,1) taking values in RR. T={T(t),t≥0}T={T(t),t≥0} is the inverse αα-stable subordinator. In this paper we extend the results obtained in M.M. Meerschaert et al. (2008) to the whole range of parameter α∈(0,1)α∈(0,1).