On one-step numerical schemes of weak convergence for SDEs with super-linear coefficients
<|reference_start|>On one-step numerical schemes of weak convergence for SDEs with super-linear coefficients: We consider weak convergence of one-step schemes for solving stochastic differential equations (SDEs) with one-sided Lipschitz conditions. It is known that the super-linear coefficients may lead to a blowup of moments of solutions and their numerical solutions. When solutions to SDEs have all finite moments, weak convergence of numerical schemes has been investigated in [Wang et al (2023), Weak error analysis for strong approximation schemes of SDEs with super-linear coefficients, IMA Journal numerical analysis]. Some modified Euler schemes have been analyzed for weak convergence. In this work, we present a family of explicit schemes of first and second-order weak convergence based on classical schemes for SDEs. We explore the effects of limited moments on these schemes. We provide a systematic but simple way to establish weak convergence orders for schemes based on approximations/modifications of drift and diffusion coefficients. We present several numerical examples of these schemes and show their weak convergence orders.<|reference_end|>
@article{zhao2024weak,
    title={Weak error analysis for strong approximation schemes of SDEs with
  super-linear coefficients II: finite moments and higher-order schemes},
    author={Yuying Zhao, Xiaojie Wang, and Zhongqiang Zhang},
    journal={arXiv preprint arXiv:2406.14065},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.14065},
    primaryClass={math.NA cs.NA math.PR}
}