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Some properties of the fractional Ornstein-Uhlenbeck process. (English) Zbl 1148.60024
The aim of the present paper is to prove some analytic properties of the so-called fractional Ornstein-Uhlenbeck process $X^H$ defined as solution of an ItĂ´-type Langevin equation driven by a fractional Brownian motion $B^H$, $0<H<1$. The authors give two-sided estimates for $\Bbb E[(X_t^H-X_s^H)^2]$ and show that $X^H$ satisfies some local non-determinism property. For a two-dimensional process, it is shown that its renormalized self-intersection local time exists in $L^2$ if and only if $0<H<3/4$.

60G15Gaussian processes
60J55Local time, additive functionals
60H05Stochastic integrals
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