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 leads naturally to:∂ An efficient algorithm to approximate the process. ∂ An ergodic theorem which applies to functionals of the type δt0ϕ(Vh(s))ds where Vh(s) = δs0h(s − u)dBu. and B is a real Brownian motion. © 1998 Applied Probability Trust.