Boundary-preserving Lamperti-splitting schemes for some Stochastic Differential Equations
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866913247300419584 |
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| author | Ulander, Johan |
| author_facet | Ulander, Johan |
| contents | 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 $p \geq 1$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_04075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary-preserving Lamperti-splitting schemes for some Stochastic Differential Equations Ulander, Johan Numerical Analysis 60H10, 60H35, 65C30 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 $p \geq 1$, 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. |
| title | Boundary-preserving Lamperti-splitting schemes for some Stochastic Differential Equations |
| topic | Numerical Analysis 60H10, 60H35, 65C30 |
| url | https://arxiv.org/abs/2308.04075 |