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

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.