  We study the dynamics of the center of mass of a Brownian particle levitated
in a Paul trap. We focus on the overdamped regime in the context of
levitodynamics, comparing theory with our numerical simulations and
experimental data from a nanoparticle in a Paul trap. We provide an exact
analytical solution to the stochastic equation of motion, expressions for the
standard deviation of the motion, and thermalization times by using the WKB
method under two different limits. Finally, we prove the power spectral density
of the motion can be approximated by that of an Ornstein-Uhlenbeck process and
use the found expression to calibrate the motion of a trapped particle.
