Fractional Brownian motion and the Markov Property

Abstract

Fractional Brownian motion belongs to a class of long memory Gaussian processes that can be represented as linear functionals of an infinite dimensional Markov process. This representation leads naturally to: - An efficient algorithm to approximate the process. - An infinite dimensional ergodic theorem which applies to functionals of the type $integra{l}_0^{t}phi(V_h(s))ds$ where $V_h(s)=integra{l}_0^{t}h(t-u)d{B}_u$ and $B$ is a standard Brownian motion.

9 pages