论文标题
随机微分方程的半污垢方法的收敛速率
Convergence rates of the Semi-Discrete method for stochastic differential equations
论文作者
论文摘要
我们研究了最初在哈里迪亚斯（2012）中提出的半二淀粉（SD）方法的收敛速率，随机微分方程和应用的半分化近似值，国际计算机数学杂志，89（6）。 SD数值方法最初是为了重现非线性随机微分方程（SDE）的定性特性。已经证明了SD方法的强收敛属性，但是除了某些类别的SDE外，该方法的顺序尚未研究。我们研究L2连接的顺序，并表明它可以任意接近1/2。理论发现由数值实验支持。
We study the convergence rates of the semi-discrete (SD) method originally proposed in Halidias (2012), Semi-discrete approximations for stochastic differential equations and applications, International Journal of Computer Mathematics, 89(6). The SD numerical method was originally designed mainly to reproduce qualitative properties of nonlinear stochastic differential equations (SDEs). The strong convergence property of the SD method has been proved, but except for certain classes of SDEs, the order of the method was not studied. We study the order of L2-convergence and show that it can be arbitrarily close to 1/2. The theoretical findings are supported by numerical experiments.
