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. 

Keywords

• subfractional Brownian motion,Ornstein-Uhlenbeck process,intersection local time

References

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