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Fractional Ornstein-Uhlenbeck processes
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Patrick Cheridito, ETH Zurich
Hideyuki Kawaguchi, Keio University and Sumitomo Mitsui Banking Corporation
Makoto Maejima, Keio University
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Abstract
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.
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Full text: PDF
Pages: 1-14
Published on: February 15, 2003
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Electronic Journal of Probability. ISSN: 1083-6489 |
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