Convergence and exponential stability of modified truncated Milstein method for stochastic differential equations

In this paper, we develop a new explicit scheme called modified truncated Milstein method which is motivated by truncated Milstein method proposed by Guo et al. (2018) and modified truncated Euler-Maruyama method introduced by Lan and Xia (2018). We obtain the strong convergence of the scheme under local boundedness and Khasminskii-type conditions, which are relatively weaker than the existing results, and we prove that the convergence rate could be arbitrarily close to 1 under given conditions. Moreover, pth moment exponential stability of the scheme is also obtained Three numerical experiments are offered to support our conclusions. & COPY; 2023 Elsevier B.V. All rights reserved.