无穷维自回归过程的中偏差原理(英文)

Moderate Deviation Principle for Infinite-dimensional Autoregressive Processes

本文考虑无穷维自回归过程经验协方差函数的中偏差原理,仅对自回归过程的随机扰动项做了高斯可积性的假设,这个条件比[4]中的对数Sobolev不等式要弱很多.主要利用了m-相依随机变量的中偏差结果和Ellis-Gartner定理,推广了[6]的结果.

A moderate deviation principle of the empirical covariance for infinite-dimensional autoregressive processes is established. The main assumption on the autoregressive process is the Gaussian integrability condition for the noise, which is weaker than the assumption of Logarithmic Sobolev Inequality in [-4]. By the moderate deviation principles of m- dependent random variables and Ellis- Gartner Theorem,we extend the results in [6].