Fractional Brownian Motion and the Markov Property

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 leads naturally to: An efficient algorithm to approximate the process.An ergodic theorem which applies to functionals of the type ∫₀ᵗ φ(Vₕ(s)),ds Vₕ(s)=∫₀ˢ h(s-u), dBᵤ,. where B is a real Brownian motion.