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