On the supremum ofγ-reflected processes with fractional Brownian motion as input

2013/06/09 by Enkelejd Hashorva, Lanpeng Ji, V. I. Piterbarg +1 · 42 citations
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #Brownian motion #Combinatorics #Discrete mathematics #Fractional Brownian motion #Gaussian #Gaussian process #Homogeneous #Infimum and supremum #Mathematics #Physics #Probability and Risk Models #Quantum mechanics #Statistics #Stochastic processes and financial applications #Stochastic processes and statistical mechanics #Zero (linguistics) #math.PR #msc:60G15 #msc:60G70

paper · pdf · doi:10.1016/j.spa.2013.06.007

published in Stochastic Processes and their Applications 123(11), 4111-4127 (Elsevier BV) · 15 pages

arxiv created 2013/06/09 · openalex publication_date 2013/06/22 · arxiv updated 2014/10/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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

Citations

• Conditional limit theorems for regulated fractional Brownian motion

Cited by

• Extremes of multifractional Brownian motion
• Extremes of a class of nonhomogeneous Gaussian random fields