论文标题
关于随机微分方程的半分化方法的渐近稳定性的注释
A note on the asymptotic stability of the Semi-Discrete method for Stochastic Differential Equations
论文作者
论文摘要
我们研究了半分化（SD）数值方法的渐近稳定性，用于近似随机微分方程。最近，我们检查了截短的SD方法的$ \ MATHCAL l^2 $ - 连接，并表明它可以任意接近$ 1/2，$参见\ textit {stamatiou，stamatiou，halidias（2019），《半污垢方法的融合速率》，用于随机差分方程的半差异方法，理论的consecontic Processes，40（40），24（40）。我们表明，截短的SD方法能够保留基础SDE的渐近稳定性。在数值示例的激励下，我们还提出了一种不同的SD方案，它使用兰佩蒂转换为原始SDE，我们称之为Lamperti Semi-Discrete（LSD）。数值模拟支持我们的理论发现。
We study the asymptotic stability of the semi-discrete (SD) numerical method for the approximation of stochastic differential equations. Recently, we examined the order of $\mathcal L^2$-convergence of the truncated SD method and showed that it can be arbitrarily close to $1/2,$ see \textit{Stamatiou, Halidias (2019), Convergence rates of the Semi-Discrete method for stochastic differential equations, Theory of Stochastic Processes, 24(40)}. We show that the truncated SD method is able to preserve the asymptotic stability of the underlying SDE. Motivated by a numerical example, we also propose a different SD scheme, using the Lamperti transformation to the original SDE, which we call Lamperti semi-discrete (LSD). Numerical simulations support our theoretical findings.
