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

08/08/2023

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by   Johan Ulander, et al.

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