Mean exit time and escape probability for the Ornstein–Uhlenbeck process

This paper studies the dynamics of the Ornstein–Uhlenbeck process by the deterministic quantities such as the mean exit time and escape probability. By solving the elliptic partial equations, we obtain explicit solutions to both mentioned problems using the special functions. We find that the mean exit time is longer for smaller noise, and the maximum depends on the middle of the given interval. Moreover, the likelihood that the solution orbits exiting the interval from left or right relies on the middle of the interval. The Monte Carlo simulations are carried out to support the obtained results.