标题： 平稳序列的希尔伯特值有界随机变量的中偏差 显示英文标题

标题： Moderate deviations for stationary sequences of Hilbert valued bounded random variables

摘要： 在本文中，我们推导了取值于希尔伯特空间的有界随机变量平稳序列的中偏差原理。 获得的条件是用鞅类型条件来表示的。 主要工具是鞅逼近和一个新的关于非适应的希尔伯特值随机变量序列的霍夫丁不等式。 给出了对Cramer-Von Mises统计量、线性过程的函数和稳定马尔可夫链的应用。 显示英文摘要

摘要： In this paper, we derive the moderate deviation principle for stationary sequences of bounded random variables with values in a Hilbert space. The conditions obtained are expressed in terms of martingale-type conditions. The main tools are martingale approximations and a new Hoeffding inequality for non adpated sequences of Hilbert-valued random variables. Applications to Cramer-Von Mises statistics, functions of linear processes and stable Markov chains are given.