A strong uniform approximation of fractional Brownian motion by means of transport processes

Abstract

We construct a sequence of processes that converges strongly to fractional Brownian motion uniformly on bounded intervals for any Hurst parameter H , and we derive a rate of convergence, which becomes better when H approaches 1 / 2 . The construction is based on the Mandelbrot–van Ness stochastic integral representation of fractional Brownian motion and on a strong transport process approximation of Brownian motion. The objective of this method is to facilitate simulation.