Intersection local time of subfractional Ornstein-Uhlenbeck processes

Year 2015, Volume: 44 Issue: 4, 975 - 990, 01.08.2015

Xiuwei Yin Guangjun Shen , Dongjin Zhu

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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