On the Supremum of gamma-reflected Processes with Fractional Brownian Motion as Input

Original · EN

Let Xₕ(t), t≥ 0 be a fractional Brownian motion with Hurst index H∈(0,1 and define a gamma-reflected process W(t)=Xₕ(t)-ct-ₛ∈[₀,ₜ](Xₕ(s)-cs), t≥0 with c>0,γ∈ [0,1] two given constants. In this paper we establish the exact tail asymptotic behaviour of ₜ∈ [₀,ₜ] Wγ(t) for any T∈ (0,]. Furthermore, we derive the exact tail asymptotic behaviour of the supremum of certain non-homogeneous mean-zero Gaussian random fields.