论文标题
$β-$混合时间序列的几乎肯定是希尔伯特空间中的$β-$混合时间序列
Almost sure invariance principle of $β-$mixing time series in Hilbert space
论文作者
论文摘要
受\ citet {berkes14}和\ citet {wu07}的启发，我们证明了固定的$β-$混合随机过程几乎确定的不变性原理。我们的结果可以应用于满足Meyn-Tweedie型Lyapunov条件的Markov链，从而将收缩条件概括为\ citet [示例2.2] {Berkes14}。我们通过大型和小块技术证明了我们的主要定理，并且嵌入的结果\ citet {gotze2011 Estimates}。我们的结果进一步应用于阵亡的马尔可夫链和功能自回归过程。
Inspired by \citet{Berkes14} and \citet{Wu07}, we prove an almost sure invariance principle for stationary $β-$mixing stochastic processes defined on Hilbert space. Our result can be applied to Markov chain satisfying Meyn-Tweedie type Lyapunov condition and thus generalises the contraction condition in \citet[Example 2.2]{Berkes14}. We prove our main theorem by the big and small blocks technique and an embedding result in \citet{gotze2011estimates}. Our result is further applied to the ergodic Markov chain and functional autoregressive processes.
