In this paper, the solution and validity of the transfer probability
density function for a stochastic dynamical system excited by white
Gaussian noise are discussed. Based on the exponential polynomial
closure method, not only the numerical solution of FPK equation is
accepted, but also the validity of the method is shown from different
views. On the one hand, the exact solution expression of the stationary
transition probability density of some kind of system is received and
its error compared with the numerical solution is analyzed. On the other
hand, by establishing a kind of potential function to observe the stable
region of the state variables in probabilistic sense, it is found that
the stable region of the state variables determined by the potential
function is highly consistent with the stable region determined by the
stationary transition probability density function after long-term
observation.