Stratonovich解释中随机微分方程积分的几种数值格式的比较
A comparison of a few numerical schemes for the integration of stochastic differential equations in the Stratonovich interpretation
摘要：
选取了三种表达式不太复杂的格式，用于Stratonovich解释下随机微分方程组的数值积分：Heun，Milstein和无导数Milstein积分法.通过比较$2^n$和$2^{n-1}$时间步长积分后的最终点，研究了每种方法的强（路径方向）收敛性。我们还比较了时间，计算机进行集成与每一个方案。把这两件事放在一起，我们得出结论，至少对于我们的系统，Heun方法是迄今为止性能最好的一个。
英文摘要：
Three schemes, whose expressions are not too complex, are selected for the numerical integration of a system of stochastic differential equations in the Stratonovich interpretation: the integration methods of Heun, Milstein, and derivative-free Milstein. The strong (path-wise) convergence is studied for each method by comparing the final points after integrating with $2^n$ and $2^{n-1}$ time steps. We also compare the time that the computer takes to carry out the integration with each scheme. Putting both things together, we conclude that, at least for our system, the Heun method is by far the best performing one.
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