论文标题
概率近似框架：马尔可夫进程方法
A probability approximation framework: Markov process approach
论文作者
论文摘要
我们在Markov过程设置中查看经典的Lindeberg原理，以建立相关的Itô公式和Markov操作员的概率近似框架。作为应用，我们研究以下三个近似值的误差界限：通过多种布朗运动，Euler-Maruyama（EM）离职的随机微分方程（SDE），近似在线随机梯度下降（SGD），用于多维Ornstein-ulnstein-ulnstein-uhlenbeck of Muoltivation of Muoltiv of Muoltiv and Importiv and Importiv。所有这些误差边界都在Wasserstein-1距离中。
We view the classical Lindeberg principle in a Markov process setting to establish a probability approximation framework by the associated Itô's formula and Markov operator. As applications, we study the error bounds of the following three approximations: approximating a family of online stochastic gradient descents (SGDs) by a stochastic differential equation (SDE) driven by multiplicative Brownian motion, Euler-Maruyama (EM) discretization for multi-dimensional Ornstein-Uhlenbeck stable process, and multivariate normal approximation. All these error bounds are in Wasserstein-1 distance.
