Numerical stationary distribution and its convergence for nonlinear stochastic differential equations

To avoid finding the stationary distributions of stochastic differential equations by solving the nontrivial Kolmogorov–Fokker–Planck equations, the numerical stationary distributions are used as the approximations instead. This paper is devoted to approximate the stationary distribution of the underlying equation by the Backward Euler–Maruyama method. Currently existing results (Mao et al., 2005; Yuan et al., 2005; Yuan et al., 2004) are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coefficient is violated.