Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 798-828.
Published online: 2017-10
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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 meanfield SDE setting. Finally some numerical examples are given to verify our theoretical results.
}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.0007}, url = {http://global-sci.org/intro/article_detail/nmtma/10457.html} }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 meanfield SDE setting. Finally some numerical examples are given to verify our theoretical results.