Strong convergence and stationary distribution of an explicit scheme for the Wright-Fisher model
Strong convergence and stationary distribution of an explicit scheme for the Wright-Fisher model
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DOI：
10.1016/j.cam.2022.115017
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发表时间：
2022-12
期刊：
影响因子：
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通讯作者：
Lin Chen;S. Gan
中科院分区：
文献类型：
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作者：
Lin Chen;S. Gan
本文设计了一种新的显式时间推进格式，称为Lamperti光滑斜率截断(LSST)格式，用于强逼近Wright-Fisher模型，该模型的系数违反Lipschitz条件，其求解过程在有界域内取值。将Lamperti型变换和光滑斜率截断相结合，构造了LSST格式。在适当的条件下，证明了LSST格式的收敛阶可达1。此外，该方案具有唯一的平稳分布，且收敛于原模型的平稳分布。数值算例证实了我们的理论发现。
A novel explicit time-stepping scheme, called Lamperti smooth sloping truncation (LSST) scheme, is devised in this paper to strongly approximate the Wright–Fisher model, whose coefficients violate the Lipschitz condition and whose solution process takes values in a bounded domain. The LSST scheme is constructed by combining the Lamperti-type transformation and the smooth sloping truncation. Under appropriate condition, it is proved that the convergence order of the LSST scheme can be up to one. Moreover, it is shown that the proposed scheme has a unique stationary distribution, which converges to that of the original model. Numerical examples are reported to confirm our theoretical findings.