The backward Euler-Maruyama method for invariant measures of stochastic differential equations with super-linear coefficients

The backward Euler-Maruyama (BEM) method is employed to approximate the invariant measure of stochastic differential equations, where both drift and diffusion coefficient are allowed grow super-linearly. existence uniqueness numerical solution generated by BEM proved convergence underlying one shown. Simulations provided illustrate theoretical results demonstrate application our in area system control.