Time characteristics of Levy flights in a steep potential well

Using the method previously developed for ordinary Brownian diffusion, we derive a new formula to calculate the correlation time of stationary L,vy flights in a steep potential well. For the symmetric quartic potential, we obtain the exact expression of the correlation time of steady-state L,vy flights with index alpha = 1. The correlation time of stationary L,vy flights decreases with an increasing noise intensity and steepness of potential well.