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Fractional Ornstein-Uhlenbeck processes

2003; Institute of Mathematical Statistics; Volume: 8; Issue: none Linguagem: Inglês

10.1214/ejp.v8-125

1083-6489

Patrick Cheridito, Hideyuki Kawaguchi, Makoto Maejima,

Statistical Mechanics and Entropy

The classical stationary Ornstein-Uhlenbeck process can be obtained in two different ways. On the one hand, it is a stationary solution of the Langevin equation with Brownian motion noise. On the other hand, it can be obtained from Brownian motion by the so called Lamperti transformation. We show that the Langevin equation with fractional Brownian motion noise also has a stationary solution and that the decay of its auto-covariance function is like that of a power function. Contrary to that, the stationary process obtained from fractional Brownian motion by the Lamperti transformation has an auto-covariance function that decays exponentially.