Correction. Central limit theorems for additive functionals of the simple exclusion process
Correction. Central limit theorems for additive functionals of the simple exclusion process
复制标题
更正。
DOI：
10.1214/009117905000000521
复制
发表时间：
2006
影响因子：
4.9
通讯作者：
S. Sethuraman
中科院分区：
文献类型：
--
作者：
By Sunder Sethuraman;S. Sethuraman
上述文件中的定义2.1是错误的。在定理2.1的证明中，它给出了满足定义2.1的某些过程的不变性原理，定义2.1中的条件足以推导出有限维收敛，但不足以应用“demartingale”的极大不等式来获得紧密性。问题是定义2.1，如前所述，只考虑了“对增量关联”，而没有考虑半鞅性质所需的更一般的关联。我们在这里稍微加强了这个定义，以使定理2.1中的紧性证明成立。下文详细介绍了如何实现这一点。用修正后的定义2.1代替之前的定义，文章中的所有结果都保持不变。特别地，命题2.1，它是定理2.1和主要结果之间的联系，并且陈述了某些可加过程满足定义2.1，具有相同的论证。
Definition 2.1 in the above paper is incorrectly stated. In the proof of Theorem 2.1, which gives an invariance principle for certain processes satisfying Definition 2.1, conditions in Definition 2.1 are sufficient to deduce finite-dimensional convergence, but not enough to apply a maximal inequality for “demimartingales” to obtain tightness. The problem is Definition 2.1, as stated, only considers “pair increment associations” and not more general associations needed for the demimartingale property. We slightly strengthen the definition here in this correction so that the proof of tightness in Theorem 2.1 holds. Details of how this is accomplished are given below. By substituting the corrected Definition 2.1 for the previous one, all results in the article hold as written. In particular, Proposition 2.1, which is the link between Theorem 2.1 and the main results, and which states certain additive processes satisfy Definition 2.1, holds with the same argument.