Fractional Ornstein-Uhlenbeck Process

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The first two moments (mean and variance) of an Ornstein–Uhlenbeck (OU) process are approximated with stochastic expansions (linear combinations of iterated integrals of the paths). The first three parameters are the usual parameters for an OU process: a high mean reversion makes the convergence to the mean faster and a high volatility increases the variance. The Hurst index controls the roughness of the fractional Brownian motion: the higher the value, the smoother the path. At Hurst index 0.5, this reduces to the usual Brownian motion.
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Contributed by: Christophe Ladroue (October 2010)
Based on a program by: Christophe Ladroue
After work by: Anastasia Papavasiliou and Christophe Ladroue
Open content licensed under CC BY-NC-SA
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References
[1] T. J. Lyons, M. J. Caruna, and T. Lévy, "Differential Equations Driven by Rough Paths," in Ecole d'eté de Probabilités de Saint-Flour, XXXIV, (J. Picard, ed.), Berlin: Springer, 2007.
[2] A. Papavasiliou and C. Ladroue, "Parameter Estimation for Rough Differential Equations." (2010) http://arxiv.org/abs/0812.3102.
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"Fractional Ornstein-Uhlenbeck Process"
http://demonstrations.wolfram.com/FractionalOrnsteinUhlenbeckProcess/
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Published: October 4 2010