论文标题
Dean-Kawasaki方程的非线性SPDE近似的弱误差分析
Weak error analysis for a nonlinear SPDE approximation of the Dean-Kawasaki equation
论文作者
论文摘要
我们考虑独立颗粒的Dean-Kawasaki方程的非线性SPDE近似。我们的近似值满足了粒子系统的物理约束，即其解决方案是所有时间的概率措施（保存阳性和质量保护）。使用双重参数，我们证明了粒子系统和非线性SPDE之间的弱误差是$ n^{ - 1-1/（d/2+1）} \ log（n）$的顺序。在此过程中，我们显示出良好的特征，比较原理和具有ITô噪声的一类非线性正规化Dean-Kawasaki方程的熵估计。关键字：院长卡瓦萨基方程，弱错误分析，拉普拉斯二重性
We consider a nonlinear SPDE approximation of the Dean-Kawasaki equation for independent particles. Our approximation satisfies the physical constraints of the particle system, i.e. its solution is a probability measure for all times (preservation of positivity and mass conservation). Using a duality argument, we prove that the weak error between particle system and nonlinear SPDE is of the order $N^{-1-1/(d/2+1)}\log (N)$. Along the way we show well-posedness, a comparison principle and an entropy estimate for a class of nonlinear regularized Dean-Kawasaki equations with Itô noise. Keywords: Dean-Kawasaki equation, weak error analysis, Laplace duality
