## Electronic Journal of Probability

### Strong approximation for additive functionals of geometrically ergodic Markov chains

#### 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 $O ( \log n)$.

#### Article information

Source
Electron. J. Probab., Volume 20 (2015), paper no. 14, 27 pp.

Dates
Accepted: 24 February 2015
First available in Project Euclid: 4 June 2016

https://projecteuclid.org/euclid.ejp/1465067120

Digital Object Identifier
doi:10.1214/EJP.v20-3746

Mathematical Reviews number (MathSciNet)
MR3317156

Zentralblatt MATH identifier
1327.60085

Subjects
Primary: 60F17: Functional limit theorems; invariance principles

Rights

#### Citation

Merlevède, Florence; Rio, Emmanuel. Strong approximation for additive functionals of geometrically ergodic Markov chains. Electron. J. Probab. 20 (2015), paper no. 14, 27 pp. doi:10.1214/EJP.v20-3746. https://projecteuclid.org/euclid.ejp/1465067120

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