关于具有变系数的显式阶1.5近似：超线性扩散系数的情况
On explicit order 1.5 approximations with varying coefficients: the case of super-linear diffusion coefficients
AI总结：
本文验证了关于通过特定方式构造高阶显式数值方案近似解的猜想，针对阶1.5的近似情况，展示了所提方法的有效性，并探讨了扩散系数的Hölder连续导数情况。
摘要：
在\cite{milsteinscheme}中出现了一个猜想，以备注的形式提出，指出可以通过特定方式构造任何高阶显式数值方案来近似具有超线性系数的SDEs的解。本文针对阶1.5的近似情况，肯定了这一猜想，并展示了所提方法的适用性。此外，本文还探讨了扩散系数具有Hölder连续导数的情况。
英文摘要：
A conjecture appears in \cite{milsteinscheme}, in the form of a remark, where it is stated that it is possible to construct, in a specified way, any high order explicit numerical schemes to approximate the solutions of SDEs with superlinear coefficients. We answer this conjecture affirmatively for the case of order 1.5 approximations and show that the suggested methodology works. Moreover, we explore the case of having Hölder continuous derivatives for the diffusion coefficients.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
