Almost sure invariance principle of β-mixing time series in Hilbert space
Abstract
Inspired by Berkes14 and 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 [Example 2.2]Berkes14. We prove our main theorem by the big and small blocks technique and an embedding result in gotze2011estimates. Our result is further applied to the ergodic Markov chain and functional autoregressive processes.
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