  In this study, we generalize the Fokker-Planck equation to two-dimensional
cases, including potential functions with periodic boundary conditions and
piecewise-defined structures, to analyze the probability distribution in
multi-field inflationary models. We employ the spectral method for spatial
derivatives and the Crank-Nicolson method for the time evolution to solve the
equation numerically for the slow-roll inflation. We find that the distribution
in the Fokker-Planck equation was determined by the two-dimensional potential
combined slow-roll parameters. And the volume weighting effect makes the
distribution in the Fokker-Planck Volume equation is determined by the
potential.
