论文标题
关于McKean-Vlasov随机微分方程的显式米尔斯坦型方案，具有超线性漂移系数
On Explicit Milstein-type Scheme for Mckean-Vlasov Stochastic Differential Equations with Super-linear Drift Coefficient
论文作者
论文摘要
我们使用有关狮子引入的测量的衍生物概念为McKean-Vlasov随机微分方程开发了一个明确的米尔斯坦型方案，并在\ cite {cardaliaguet2013}中进行了讨论。允许漂移系数在空间变量中超级线性生长。此外，假定漂移和扩散系数仅在与空间和度量相对应的变量中可区分一次。强烈的收敛速度显示出等于$ 1.0 $，而无需使用ITô的公式来取决于度量。由于系数对测量的依赖而引起的挑战是解决的，我们的发现与随机微分方程的类似结果一致。
We develop an explicit Milstein-type scheme for McKean-Vlasov stochastic differential equations using the notion of derivative with respect to measure introduced by Lions and discussed in \cite{cardaliaguet2013}. The drift coefficient is allowed to grow super-linearly in the space variable. Further, both drift and diffusion coefficients are assumed to be only once differentiable in variables corresponding to space and measure. The rate of strong convergence is shown to be equal to $1.0$ without using Itô's formula for functions depending on measure. The challenges arising due to the dependence of coefficients on measure are tackled and our findings are consistent with the analogous results for stochastic differential equations.
