The Semi-tamed Milstein Method For Commutative Stochastic Differential Equations With Nonglobally Lipschitz Continuous Coefficients

In recent years,the application of stochastic differential equations(SDEs)in various fields has become more and more extensive,the research on numerical solution is more and more urgent.For SDEs with a superlinearly growing and globally one-sided Lipschitz con-tinuous drift coefficient,the explicit Euler scheme fails to converge strongly to the exact solution,the implicit Euler scheme is known to converge strongly to the exact solution,however,require additional computation effort.To solve this problem,recently,tamed Eu-ler scheme,tamed Milstein scheme and semi-tamed Euler scheme were proposed by some author.These method are explicit,and their numerical solutions can converge to exact solu-tion.Motivated by these method,we here introduce a semi-tamed version of the Milstein scheme for SDEs with commutative noise.The proposed method is also explicit and easily implementable.Moreover,this paper will prove that the numerical solution can converge to the exact solution with the order of 1.