Electronic Journal of Probability

Strong approximation for additive functionals of geometrically ergodic Markov chains

Florence Merlevède and Emmanuel Rio

Full-text: Open access

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

Permanent link to this document
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

Keywords
dditive functionals Markov chains Renewal processes Partial sums Harris recurrent Strong mixing Absolute regularity Geometric ergodicity Invariance principle Strong approximation

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

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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