@Article{NMTMA-10-798,
author = {Yabing Sun, Jie Yang and Weidong Zhao},
title = {Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations},
journal = {Numerical Mathematics: Theory, Methods and Applications},
year = {2017},
volume = {10},
number = {4},
pages = {798--828},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2079-7338},
doi = {https://doi.org/10.4208/nmtma.2017.0007},
url = {http://global-sci.org/intro/article_detail/nmtma/10457.html}
}