Split-step balanced θ-method for SDEs with non-globally Lipschitz continuous coefficients

作者：

Highlights：

• It is proved that under some non-global Lipschitz conditions the SSBT scheme is convergent with order 0.5 in strong sense.

• The presented SSBT scheme can preserve the exponential stability of the exact solution.

• The technique we presented in Lemma 4.2 and Theorem 4.4 can be generalized for proving stability of other schemes.

摘要

•It is proved that under some non-global Lipschitz conditions the SSBT scheme is convergent with order 0.5 in strong sense.•The presented SSBT scheme can preserve the exponential stability of the exact solution.•The technique we presented in Lemma 4.2 and Theorem 4.4 can be generalized for proving stability of other schemes.

论文关键词：Nonlinear problems,The balanced method,Strong convergence,Exponential stability,Mean-square contraction

论文评审过程：Received 26 December 2020, Revised 24 May 2021, Accepted 2 June 2021, Available online 20 September 2021, Version of Record 20 September 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.126437