Truncated Milstein method for non-autonomous stochastic differential equations and its modification
Numerical Analysis
2021-04-28 v2 Numerical Analysis
Probability
Abstract
The truncated Milstein method, which was initially proposed in (Guo, Liu, Mao and Yue 2018), is extended to the non-autonomous stochastic differential equations with the super-linear state variable and the H\"older continuous time variable. The convergence rate is proved. Compared with the initial work, the requirements on the step-size is also significantly released. In addition, the technique of the randomized step-size is employed to raise the convergence rate of the truncated Milstein method.
Cite
@article{arxiv.2011.00023,
title = {Truncated Milstein method for non-autonomous stochastic differential equations and its modification},
author = {Juan Liao and Wei Liu and Xiaoyan Wang},
journal= {arXiv preprint arXiv:2011.00023},
year = {2021}
}
Comments
25 pages, 2 figures