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2003 Fractional Ornstein-Uhlenbeck processes
Patrick Cheridito, Hideyuki Kawaguchi, Makoto Maejima
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Electron. J. Probab. 8: 1-14 (2003). DOI: 10.1214/EJP.v8-125


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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Patrick Cheridito. Hideyuki Kawaguchi. Makoto Maejima. "Fractional Ornstein-Uhlenbeck processes." Electron. J. Probab. 8 1 - 14, 2003.


Published: 2003
First available in Project Euclid: 23 May 2016

zbMATH: 1065.60033
MathSciNet: MR1961165
Digital Object Identifier: 10.1214/EJP.v8-125

Primary: 60H10
Secondary: 45F05‎ , 60G15 , 60G18

Keywords: fractional Brownian motion , Lampertitransformation , Langevin equation , long-range dependence , selfsimilar processes

Rights: Copyright © 2003 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • 2003
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