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Fractional Ornstein-Uhlenbeck processes

   
@article{EJP125,
	author = {Patrick Cheridito and Hideyuki Kawaguchi and Makoto Maejima},
	title = {Fractional Ornstein-Uhlenbeck processes},
	journal = {Electron. J. Probab.},
	fjournal = {Electronic Journal of Probability},
	volume = {8},
	year = {2003},
	keywords = {Fractional Brownian motion, Langevin equation,Long-range dependence, Selfsimilar processes, Lampertitransformation},
	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.},
	pages = {no. 3, 1-14},
	issn = {1083-6489},
	doi = {10.1214/EJP.v8-125},    
        url = {http://ejp.ejpecp.org/article/view/125}}