We propose and analyse an explicit boundary-preserving scheme for the strong approximations of some SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The scheme consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\Omega)$-convergence of order $1$, for every $p \in \mathbb{N}$, of the scheme and exploit the Lamperti transform to confine the numerical approximations to the state-space of the considered SDE. We provide numerical experiments that confirm the theoretical results and compare the proposed Lamperti-splitting scheme to other numerical schemes for SDEs.

翻译：我们提出并分析了一种显式边界保持格式，用于对状态空间有界且漂移与扩散系数非全局Lipschitz的某些随机微分方程进行强近似。该格式由Lamperti变换后接Lie-Trotter分裂构成。我们证明了该格式对每个$p \in \mathbb{N}$具有$L^{p}(\Omega)$-收敛阶为1，并利用Lamperti变换将数值近似限制在所讨论随机微分方程的状态空间内。我们提供的数值实验证实了理论结果，并将所提出的Lamperti分裂格式与其他随机微分方程数值格式进行了比较。