Yan, Litan; Lu, Yunsheng; Xu, Zhiqiang Some properties of the fractional Ornstein-Uhlenbeck process. (English) Zbl 1148.60024 J. Phys. A, Math. Theor. 41, No. 14, Article ID 145007, 17 p. (2008). 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 \(0<H<3/4\). Reviewer: Werner Linde (Jena) Cited in 4 Documents MSC: 60G15 Gaussian processes 60J55 Local time and additive functionals 60H05 Stochastic integrals Keywords:fractional Brownian motion; Ornstein-Uhlenbeck process; local non-determinism; local time PDFBibTeX XMLCite \textit{L. Yan} et al., J. Phys. A, Math. Theor. 41, No. 14, Article ID 145007, 17 p. (2008; Zbl 1148.60024) Full Text: DOI