Numerical Integration of Stochastic Differential Equations with Nonglobally Lipschitz Coefficients

We propose a new concept which allows us to apply any numerical method of weak approximation to a very broad class of stochastic differential equations (SDEs) with nonglobally Lipschitz coefficients. Following this concept, we discard the approximate trajectories which leave a sufficiently large sphere. We prove that accuracy of any method of weak order p is estimated by ε + O(hp), where ε can be made arbitrarily small with increasing radius of the sphere. The results obtained are supported by numerical experiments.