Estimates for moments of supremum of reflected fractional Brownian motion

TL;DR

This paper derives bounds for the moments of the supremum of reflected fractional Brownian motion, which are useful for understanding maximal inequalities in stochastic processes.

Contribution

It provides new bounds for the expected moments of the supremum of fractional Brownian motion, extending previous results in the field.

Findings

Derived bounds for E[sup_{t in [0,T]} |B_H(t)|]^γ

Applicable to various Hurst parameters H and moments γ

Enhances understanding of maximal inequalities for fractional Brownian motion

Abstract

Let $B_H(\cdot)$ be a fractional Brownian motion with Hurst parameter $H\in(0,1]$. Motivated by applications to maximal inequalities for fractional Brownian motion, in this note we derive bounds for K_T(H,\gamma):=E[\sup_{t\in[0,T]}|B_H(t)|]^\gamma, with $\gamma, T>0$.