Abstract: The finite element method was used to solve the probability density function with periodic properties to study the statistical properties of stochastic periodic solutions. We proved the integral conservation of the full space approximate solution and the spatial integral approximate conservation of the approximate solution truncated to a finite interval, and verified  the effectiveness of the method  by numerical experiments.

Key words: stochastic differential equation, stochastic periodic solution in distribution, Fokker-Planck equation, finite element method, approximate conservation