Abstract
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.
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