论文标题
完全耦合随机微分方程的扩散近似
Diffusion approximation for fully coupled stochastic differential equations
论文作者
论文摘要
我们考虑$ \ mathbb r^d $中的泊松方程，用于对应于ergodic扩散过程的椭圆操作员。相对于参数的最佳规律性和平滑度是在系数的轻度条件下获得的。然后，将结果应用于建立仅具有Hölder连续系数的完全耦合多时间尺度随机微分方程的一般扩散近似。获得了四个不同的平均方程以及收敛速率。此外，收敛性仅依赖于慢变量系数的规律性，并且不取决于它们相对于快速分量的规律性。
We consider a Poisson equation in $\mathbb R^d$ for the elliptic operator corresponding to an ergodic diffusion process. Optimal regularity and smoothness with respect to the parameter are obtained under mild conditions on the coefficients. The result is then applied to establish a general diffusion approximation for fully coupled multi-time-scales stochastic differential equations with only Hölder continuous coefficients. Four different averaged equations as well as rates of convergence are obtained. Moreover, the convergence is shown to rely only on the regularities of the coefficients with respect to the slow variable, and does not depend on their regularities with respect to the fast component.
