Intersection local time of subfractional Ornstein-Uhlenbeck processes

Authors : Xiuwei YİN, Guangjun SHEN, Dongjin ZHU

Pages : 975-990

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Publication Date : 2015-08-01

Article Type : Research Paper

Abstract :In this paper, we consider Ornstein-Uhlenbeck process d X t H = − X t H  d t +  v d S t H ,  X 0 H = x, driven by a subfractional Brownian motion S H . We prove that the subfractional Ornstein-Uhlenbeck process X H 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, X H and $\tilde{ X}^H$ , exists in  L 2   if and only if  Hd< 2 . 
Keywords : subfractional Brownian motion, Ornstein Uhlenbeck process, intersection local time