Approximation of fractional Brownian motion by martingales

Abstract

We study the problem of optimal approximation of a fractional Brownian motion by martingales. We prove that there exist a unique martingale closest to fractional Brownian motion in a specific sense. It shown that this martingale has a specific form. Numerical results concerning the approximation problem are given.

Cited by in corpus (2)

• Weak convergence of path-dependent SDEs driven by fractional Brownian motion with irregular coefficients
• Distance from fractional Brownian motion with associated Hurst index $0<H<1/2$ to the subspaces of Gaussian martingales involving power integrands with an arbitrary positive exponent