Research On Euler Method For Stochastic Differential Equations

In this work, we study a class of modified Euler methods applied to a family of SDEs with deterministic diffusion coefficients with respect to time t. And we give a convergence result for modified Euler method requiring that the SDE is globally Lip-schitz. Then we discuss the strong convergence of Modified Euler Scheme under the assumptions that the drift coefficient of SDE satisfies locally Lipschitz condition as well as one-sided Lipschitz condition.Finally, through numerical experiment, we observe that the Modified Euler Method is more accurate than classical Euler Method.