论文标题
布朗运动与戈德斯坦 - KAC电报过程之间的瓦斯汀距离的定量控制
Quantitative control of Wasserstein distance between Brownian motion and the Goldstein--Kac telegraph process
论文作者
论文摘要
在本手稿中，我们通过二次平均成本的瓦斯尔斯坦距离提供了电报过程与布朗运动之间的非肌电过程水平控制。此外，我们得出了相应的时间平均$ p $ - thments的非反应估计。证明依赖于耦合技术，例如旋转耦合，同步耦合和komlós--major--tusnády耦合。
In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with quadratic average cost. In addition, we derive non-asymptotic estimates for the corresponding time average $p$-th moments. The proof relies on coupling techniques such as coin-flip coupling, synchronous coupling and the Komlós--Major--Tusnády coupling.
