TY - JOUR
T1 - Itô-Taylor Schemes for Solving Mean-Field Stochastic Differential Equations
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 798
EP - 828
PY - 2017
DA - 2017/10
SN - 10
DO - http://doi.org/10.4208/nmtma.2017.0007
UR - https://global-sci.org/intro/article_detail/nmtma/10457.html
KW - Itô-Taylor scheme, mean-field stochastic differential equation, mean-field Itô-Taylor
formula, error estimate.
AB - <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>