Boundary-preserving Lamperti-splitting schemes for some stochastic differential equations

Abstract

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 (Ω)convergence of order 1, for every p ≥ 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.