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:Zhao, W(wdzhao@sdu.edu.cn)
通讯作者地址:[Zhao, WD]Shandong Univ, Sch Math, Jinan 250100, Shandong, Peoples R China.
来源:高等学校计算数学学报
出版年:2017
卷:10
期:4
页码:798-828
DOI:10.4208/nmtma.2017.0007
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.
收录类别:CSCD;SCOPUS;SCIE
资源类型:期刊论文
原文链接:https://www.scopus.com/inward/record.uri?eid=2-s2.0-85029939448&doi=10.4208%2fnmtma.2017.0007&partnerID=40&md5=398e017b74560c008efdccbcf8887df8
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