Fractional Brownian Motion and the Markov Property
Philippe Carmona, Université Paul Sabatier
Laure Coutin, Université Paul Sabatier
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
$$int_0^t phi(V_h(s)),ds quadtext{where}quad V_h(s)=int_0^s h(s-u), dB_u,.$$
where $B$ is a real Brownian motion.
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