A fundamental mean-square convergence theorem for SDEs with locally Lipschitz coefficients and its applications

A version of the fundamental mean-square convergence theorem is proved for stochastic differential equations (SDE) which coefficients are allowed to grow polynomially at infinity and which satisfy a one-sided Lipschitz condition. The theorem is illustrated on a number of particular numerical methods, including a special balanced scheme and fully implicit methods. Some numerical tests are presented.