Stein's method for Brownian approximations
Stein's method for Brownian approximations
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布朗近似的 Stein 方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
L. Decreusefond
中科院分区：
文献类型：
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作者：
L. Coutin;L. Decreusefond
本文受Barthel的一个定理的启发，从Stein方法的观点出发，重新讨论了概率论中的一些经典极限定理。我们建立了一个框架来约束无限维空间上某些分布之间的Wasserstein距离。我们证明了布朗运动的泊松近似的收敛速度与$\lambda^{-1/2}$成正比，其中$\lambda$是泊松过程的强度。我们还展示了收敛速度的Donsker定理和布朗运动的线性插值。通过迭代过程，我们给出了具有精确误差界的Edgeworth展开式。
Motivated by a theorem of Barbour, we revisit some of the classical limit theorems in probability from the viewpoint of the Stein method. We setup the framework to bound Wasserstein distances between some distributions on infinite dimensional spaces. We show that the convergence rate for the Poisson approximation of the Brownian motion is as expected proportional to $\lambda^{-1/2}$ where $\lambda$ is the intensity of the Poisson process. We also exhibit the speed of convergence for the Donsker Theorem and for the linear interpolation of the Brownian motion. By iterating the procedure, we give Edgeworth expansions with precise error bounds.