A Lower Bound for the First Passage Time Density of the Suprathreshold Ornstein-Uhlenbeck Process

Peter J. Thomas

We prove that the first passage time density $\rho (t)$ for an Ornstein-Uhlenbeck process $X(t)$ obeying $dX=-\beta Xdt+\sigma dW$ to reach a fixed threshold $\theta$ from a suprathreshold initial…