论文标题
对于某些类别的非平稳混合序列的几乎肯定的不变性原理
An almost sure invariance principle for some classes of non-stationary mixing sequences
论文作者
论文摘要
在本说明中，我们（特别是）证明了几乎确定的不变性原理（ASIP），对于随机变量的非平稳和统一界限序列，这些变量是指数级快速$ ϕ $ - 混合的。所获得的费率为$ o（v_n^{\ frac14+\ del}）$对于任意$ \ del> 0 $，其中$ v_n $是基础部分总和$ s_n $的方差。对于某些类别不均匀的马尔可夫链，我们还证明了具有相似速率的矢量值ASIP。
In this note we (in particular) prove an almost sure invariance principle (ASIP) for non-stationary and uniformly bounded sequences of random variables which are exponentially fast $ϕ$-mixing. The obtained rate is of order $o(V_n^{\frac14+\del})$ for an arbitrary $\del>0$, where $V_n$ is the variance of the underlying partial sums $S_n$. For certain classes of inhomogeneous Markov chains we also prove a vector-valued ASIP with similar rates.
