Intersection local time of subfractional Ornstein-Uhlenbeck processes

Abstract

In this paper, we consider Ornstein-Uhlenbeck process dXtH =−XtH dt+ vdStH, X0H =x, driven by a subfractional Brownian motion S H . We prove that the subfractional Ornstein-Uhlenbeck process XH is local nondeterministic and give some properties of this process. As an application, assume d ≥ 2, we prove that the intersection local time of two independent, d−dimensional subfractional Ornstein-Uhlenbeck process,XH and $\tilde{X}^H$, exists in L2 if and only if Hd<2.