摘要 : In this paper, we introduce a split-step theta Milstein (SSTM) method for n-dimensional stochastic delay differential equations (SDDEs). The exponential mean-square stability of the numerical solutions is analyzed, and in accordan... 展开 In this paper, we introduce a split-step theta Milstein (SSTM) method for n-dimensional stochastic delay differential equations (SDDEs). The exponential mean-square stability of the numerical solutions is analyzed, and in accordance with previous findings, we prove that the method is exponentially mean-square stable if the employed time-step is smaller than a given and easily computable upper bound. In particular, according to our investigation, larger time-steps can be used in the case theta is an element of (1/2, 1] than in the case theta is an element of [0, 1/2]. Numerical results are presented which reveal that the SSTM method is conditionally mean-square stable and that in the case theta is an element of(1/2, 1] the interval of time-steps for which the SSTM method is theoretically shown to be mean-square stable is significantly larger than in the case theta is an element of [0, 1/2]. It is worth mentioning that the SSTM method has never been employed or analyzed for the numerical approximation of SDDEs, at least to the very best of our knowledge. (C) 2018 Elsevier Inc. All rights reserved. 收起