无穷维自回归过程的中偏差原理

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-Grtner定理,推广了[6]的结果.

Moderate Deviation Principle for Infinite-dimensional Autoregressive Processes

A moderate deviation principle of the empirical covariance for infinite-dimensional autore-gressive 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 . By the moderate deviation principles of m- dependent random variables and Ellis-Gartner Theorem,we extend the results in .