论文标题
在非平稳设置中的Eagleson定理上
On Eagleson's theorem in the non-stationary setup
论文作者
论文摘要
经典的Eagleson定理指出，如果适当地归一化的Birkhoff总和由可测量函数产生和保留转换的概率在分布中收敛，则它们还相对于任何概率度量，这对于相对于不变的任何概率绝对连续。在此简短说明中，我们证明了Eagleson定理的几个版本，用于某些类别的非平稳随机过程，这些过程满足了某些类型的相关性衰减。
The classical Eagleson's theorem states that if appropriately normalized Birkhoff sums generated by a measurable function and a probability preserving transformation converge in distribution, then they also converge in distribution with respect to any probability measure which is absolutely continuous with respect to the invariant one. In this short note we prove several versions of Eagleson's theorem for some classes of non-stationary stochastic processes which satisfy certain type of decay of correlations.
