Year: 2017
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 4 : pp. 798–828
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 meanfield SDE setting. Finally some numerical examples are given to verify our theoretical results.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.2017.0007
Numerical Mathematics: Theory, Methods and Applications, Vol. 10 (2017), Iss. 4 : pp. 798–828
Published online: 2017-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 31
Keywords: Itô-Taylor scheme mean-field stochastic differential equation mean-field Itô-Taylor formula error estimate.
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