Some properties of the fractional Ornstein–Uhlenbeck process**The project is sponsored by NSFC (10571025) and the Key Project of Chinese Ministry of Education (no 106076).

Abstract

We consider the fractional analogue of the Ornstein–Uhlenbeck process, i.e. the solution of the Langevin equation driven by a fractional Brownian motion in place of the usual Brownian motion. We establish some properties of these processes. We show that the process is local nondeterminism. For a two-dimensional process we show that its renormalized self-intersection local time exists in L2 if and only if .