We propose and analyse boundary-preserving schemes for the strong approximations of some scalar SDEs with non-globally Lipschitz drift and diffusion coefficients whose state-space is bounded. The schemes consists of a Lamperti transform followed by a Lie--Trotter splitting. We prove $L^{p}(\Omega)$-convergence of order $1$, for every $p \geq 1$, of the schemes 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 schemes to other numerical schemes for SDEs.

翻译：我们提出并分析用于某些标量SDE（随机微分方程）强近似问题的边界保持格式，这些SDE具有非全局利普希茨漂移和扩散系数，且其状态空间有界。该格式基于Lamperti变换与Lie--Trotter分裂相结合。我们证明了对于任意$p \geq 1$，该格式具有$L^{p}(\Omega)$-收敛阶为1，并利用Lamperti变换将数值近似限制在所考虑SDE的状态空间内。提供的数值实验验证了理论结果，并将所提出的Lamperti分裂格式与其他SDE数值格式进行了比较。