论文标题
反射的布朗动作的无维度局部收敛和扰动
Dimension-free local convergence and perturbations for reflected Brownian motions
论文作者
论文摘要
我们在$ \ mathbb {r}^d _+$中描述并分析了一类正面反射反射的布朗动作（RBMS），其本地统计信息以与尺寸$ d $无关的速率融合到平衡。在反射矩阵，漂移和扩散系数的合适假设下，通过估计同步耦合的rbms之间的基本加权距离的收缩，可以获得尺寸独立的拉伸指数收敛速率。我们还研究对称地图集模型是获得不满足上述假设的RBM的维度无关收敛速率的第一步。通过分析路径衍生过程并将其连接到随机环境中的随机行走，我们获得了对称地图集模型的间隙过程的多项式收敛速率，从适当的平稳性扰动开始。
We describe and analyze a class of positive recurrent reflected Brownian motions (RBMs) in $\mathbb{R}^d_+$ for which local statistics converge to equilibrium at a rate independent of the dimension $d$. Under suitable assumptions on the reflection matrix, drift and diffusivity coefficients, dimension-independent stretched exponential convergence rates are obtained by estimating contractions in an underlying weighted distance between synchronously coupled RBMs. We also study the Symmetric Atlas model as a first step in obtaining dimension-independent convergence rates for RBMs not satisfying the above assumptions. By analyzing a pathwise derivative process and connecting it to a random walk in a random environment, we obtain polynomial convergence rates for the gap process of the Symmetric Atlas model started from appropriate perturbations of stationarity.
