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Fractional Brownian motion and the Markov Property

Philippe Carmona·Laure Coutin
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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 $integral_0^t phi(V_h(s)) ds $ where $V_h(s)=integral_0^t h(t-u) dB_u$ and $B$ is a standard Brownian motion.

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Philippe Carmona, Laure Coutin. 1998-09-22. Fractional Brownian motion and the Markov Property. https://arxiv.org/abs/math/9809123

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