论文标题
平均场随机微分方程的数值方法
Numerical methods for mean-field stochastic differential equations with jumps
论文作者
论文摘要
在本文中，我们专门研究具有跳跃（MSDEJS）的平均场随机微分方程的数值方法。首先，使用平均田间公式[Sun，Yang和Zhao，Numer。数学。理论。冰毒。 Appl。，10（2017），pp。〜798--828]，我们开发了Itô公式并为MSDEJS构建了Itô-Taylor的扩展。然后，根据itô-taylor的扩展，我们提出了强订单$γ$和MSDEJS的弱订单$η$itô-taylor计划。从理论上讲，我们从理论上证明了强大和弱的融合率$γ$和$η$的强大和弱的Itô-Taylor计划。最后，还提出了一些数值测试，以验证我们的理论结论。
In this paper, we are devoted to the numerical methods for mean-field stochastic differential equations with jumps (MSDEJs). First by using the mean-field Itô formula [Sun, Yang and Zhao, Numer. Math. Theor. Meth. Appl., 10 (2017), pp.~798--828], we develop the Itô formula and construct the Itô-Taylor expansion for MSDEJs. Then based on the Itô-Taylor expansion, we propose the strong order $γ$ and the weak order $η$ Itô-Taylor schemes for MSDEJs. %We theoretically prove The strong and weak convergence rates $γ$ and $η$ of the strong and weak Itô-Taylor schemes are theoretically proved, respectively. Finally some numerical tests are also presented to verify our theoretical conclusions.
