Large deviations for subordinated fractional Brownian motion and applications

• DOI: 10.1016/j.jmaa.2017.10.035
• Publication Date: 2017-10-19T05:30:55Z
• Authors: Weigang Wang; Zhenlong Chen
• Keywords: Fractional Brownian motion; Brownian excursion; Reflected Brownian motion

Abstract Let W H = { W H ( t ) , t ∈ R } be a real valued fractional Brownian motion with Hurst index H ∈ ( 0 , 1 ) and let T = { T t , t ≥ 0 } be an inverse α-stable subordinator independent of W H . The inverse stable subordinator fractional Brownian motion Z H = { Z H ( t ) , t ≥ 0 } is defined by Z H ( t ) = W H ( T t ) , 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 Z H and its supremum process. And we also give asymptotic properties of the tail probability of the supremum process.