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Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations

  • Yabing Sun (a1), Jie Yang (a1) and Weidong Zhao (a1)
Abstract
Abstract

This paper is devoted to numerical methods for mean-field stochastic differential equations (MSDEs). We first develop the mean-field Itô formula and mean-field Itô-Taylor expansion. Then based on the new formula and expansion, we propose the Itô-Taylor schemes of strong order γ and weak order η for MSDEs, and theoretically obtain the convergence rate γ of the strong Itô-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.

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*Corresponding author. Email addresses: sunybly@163.com (Y. B. Sun), yangjie218@mail.sdu.edu.cn (J. Yang), wdzhao@sdu.edu.cn (W. D. Zhao)
References
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Numerical Mathematics: Theory, Methods and Applications
  • ISSN: 1004-8979
  • EISSN: 2079-7338
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