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

Boundary-preserving Lamperti-splitting scheme for some Stochastic Differential Equations