标题：Ito-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations
作者：Sun Yabing;Yang Jie;Zhao Weidong
作者机构：[Sun Yabing] School of Mathematics & Finance Institute, Shandong University, Jinan, Shandong 250100, China.;[Yang Jie] School of Mathematics & Finance 更多
通讯作者地址：[Zhao, WD]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
关键词：Ito-Taylor scheme; mean-field stochastic differential equation;; mean-field Ito-Taylor formula; error estimate
摘要：This paper is devoted to numerical methods for mean-field stochastic differential equations (MSDEs). We first develop the mean-field Ito formula and mean-field Ito-Taylor expansion. Then based on the new formula and expansion, we propose the Ito-Taylor schemes of strong order gamma and weak order eta for MSDEs, and theoretically obtain the convergence rate gamma of the strong Ito-Taylor scheme, which can be seen as an extension of the well-known fundamental strong convergence theorem to the mean-field SDE setting. Finally some numerical examples are given to verify our theoretical results.