A note on convergence and stability of the truncated Milstein method for stochastic differential equations
arXiv:1809.059932 citations
Originality Synthesis-oriented
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For researchers in numerical SDEs, this is an incremental improvement to an existing method.
The paper relaxes step-size constraints for the truncated Milstein method for SDEs and proves its almost sure stability, supported by numerical simulations.
Some new techniques are employed to release significantly the requirements on the step size of the truncated Milstein method, which was originally developed in Guo, Liu, Mao and Yue (2018). The almost sure stability of the method is also investigated. Numerical simulations are presented to demonstrate the theoretical results.