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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 Itô-type Langevin equation driven by a fractional Brownian motion \(B^H\), \(0<H<1\). The authors give two-sided estimates for \(\mathbb E[(X_t^H-X_s^H)^2]\) 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 \(0<H<3/4\).

MSC:

60G15 Gaussian processes
60J55 Local time and additive functionals
60H05 Stochastic integrals
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