Almost sure invariance principle of β-mixing time series in Hilbert space

2022/09/26 by Jianya Lu, Wei Biao Wu, Lu, Jianya +5
Computer Science · Mathematics · #Bayesian Modeling and Causal Inference #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Probability (math.PR) #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2209.12535

openalex publication_date 2022/09/26 · openalex created_date 2022/09/28 · openalex updated_date 2026/07/28

Abstract

Inspired by \citetBerkes14 and \citetWu07, 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 \citetgotze2011estimates. Our result is further applied to the ergodic Markov chain and functional autoregressive processes.

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