Abstract
Let $(\xi_i)_{i \in {\mathbb Z}}$ be a stationary Harris recurrent geometrically erodic Markov chain on a countably generated state space $(E, {\mathcal B})$. Let $f$ be a bounded and measurable function from $E$ into ${\mathbb R}$ satisfying the condition ${\mathbb E} ( f ( \xi_0))=0$. In this paper, we obtain the almost sure strong approximation of the partial sums $S_n(f) = \sum_{i=1}^n f ( \xi_i)$ by the partial sums of a sequence of independent and identically distributed Gaussian random variables with the optimal rate $O ( \log n)$.
Citation
Florence Merlevède. Emmanuel Rio. "Strong approximation for additive functionals of geometrically ergodic Markov chains." Electron. J. Probab. 20 1 - 27, 2015. https://doi.org/10.1214/EJP.v20-3746
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