Fractional Brownian motion and the Markov Property

الأصل · EN

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 integral₀ᵗ phi(Vₕ(s)) ds where Vₕ(s)=integral₀ᵗ h(t-u) dBᵤ and B is a standard Brownian motion.