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 [21, 31, 33] are extended in this paper to cover larger range of nonlinear SDEs when the linear growth condition on the drift coeffcient is violated.
- the backward Euler-Maruyama method
- weak convergence
- numerical stationary distribution
- nonlinear SDEs