论文标题
Donsker定理用于多维周期性扩散的职业度量
Donsker Theorems for Occupation Measures of Multi-Dimensional Periodic Diffusions
论文作者
论文摘要
我们研究了随着周期性漂移和扩散率的多维扩散过程产生的经验过程。利用扩散的发电机的平滑性能来证明某些类别的平滑功能的Donsker属性。我们从[van der Vaart＆van Zanten，2005]中研究的一维情况中部分概括了发现：扩散经验过程比I.I.D.的经典案例表现出更强的规律性。观察。作为一种应用，针对时间-1 $ t $占用度量与尺寸$ d \ d \ leq3 $之间的wasserstein-1距离进行了精确的渐近学。
We study the empirical process arising from a multi-dimensional diffusion process with periodic drift and diffusivity. The smoothing properties of the generator of the diffusion are exploited to prove the Donsker property for certain classes of smooth functions. We partially generalise the finding from the one-dimensional case studied in [van der Vaart & van Zanten, 2005]: that the diffusion empirical process exhibits stronger regularity than in the classical case of i.i.d. observations. As an application, precise asymptotics are deduced for the Wasserstein-1 distance between the time-$T$ occupation measure and the invariant measure in dimensions $d\leq3$.
