论文标题
从随机最大不等式到无限维数
From a stochastic maximal inequality to infinite-dimensional martingales
论文作者
论文摘要
作为在随机场研究中开发的众所周知的“链接”和“括号”方法的替代方法，提出了一种基于使用泰勒膨胀得出的随机最大不平等的新方法。通过使用单调融合论证，与有限维离散时间的不平等现象相关的不平等现象将提高到无限维度。主要的结果是在均匀拓扑结构下，在熵方法的帮助下，在均匀拓扑结构下，离散时间mar的可分离随机场序列的弱收敛定理。作为特殊情况，I.I.D.的一些新结果获得了随机序列，包括新的Donsker定理和一刻，以通过集合或函数类索引的经验过程绑定。
As an alternative to the well-known methods of "chaining" and "bracketing" that have been developed in the study of random fields, a new method, which is based on a stochastic maximal inequality derived by using the Taylor expansion, is presented. The inequality dealing with finite-dimensional discrete-time martingales is pulled up to infinite-dimensional ones by using the monotone convergence arguments. The main results are some weak convergence theorems for sequences of separable random fields of discrete-time martingales under the uniform topology with the help also of entropy methods. As special cases, some new results for i.i.d. random sequences, including a new Donsker theorem and a moment bound for suprema of empirical processes indexed by classes of sets or functions, are obtained.
