The Local Time of the Fractional Ornstein-Uhlenbeck Process

Abstract

We investigate the Hölder regularity of the local time of the fractional Ornstein-Uhlenbeck process $X^H=\{X_t^H,t\ge 0\}$. As a related problem, we study the collision local time of two independent fractional Ornstein-Uhlenbeck $X^{H_i}=\{X_t^{H_i},t\ge 0\}$, $i=1,2$ with respective indices $H_1,H_2\in (0,1)$.