Non-gaussianity from multi-field stochastic inflation

We have investigated the Statistical nature of the multi-field inflation with the stochas tic approach, in wbich the evolution of the scalar fields is described by the Langevin equations. To solve the corresponding Fokker-Planck equation analytically, we adopt the technique of the scaling approximation. We have improved the previotis investi- gation [Amendola, 1993] requiring the probability funetion to have the symmetry in exchanging the field Parameters. We have investigated the non-Gaussian nature of the probability funetion by decomposing the fields into the adiabatic and the isocurvature components. We find that the non-Gaussianity of the isocurvature component can be large compared with that of the adiabatic component. The adiabatic and isocurvature components may be correlated at nonlinear order in the skewness and kurtosis even if uncorrelated at linear level. To check the results, we perform numerical Simulation of the distribution funetion by solving the Langevin equation repeatedly.