Estimates for moments of supremum of reflected fractional Brownian motion

2009/12/16 by Krzysztof Dȩbicki, Debicki, Krzysztof, Agata Tomanek +1
Economics, Econometrics and Finance · Mathematics · #60G15 (Primary) #60G70 (Secondary) #68M20 #FOS: Mathematics #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.0912.3117

openalex publication_date 2009/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let B_H(⋅) be a fractional Brownian motion with Hurst parameter H∈(0,1]. Motivated by applications to maximal inequalities for fractional Brownian motion, in this note we derive bounds for K_T(H,γ):=E[sup_t∈[0,T]|B_H(t)|]^γ, with γ, T>0.

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