## Electronic Communications in Probability

### Identification of the rate function for large deviations of an irreducible Markov chain

#### Abstract

For an irreducible Markov chain $(X_n)_{n\ge 0}$ we identify the rate function governing the large deviation estimation of empirical mean $\frac {1}{n} \sum_{k=0}^{n-1} f(X_k)$ by means of the Donsker-Varadhan's entropy. That allows us to obtain the lower bound of large deviations for the empirical measure $\frac {1}{n} \sum_{k=0}^{n-1} \delta_{X_k}$ in full generality

#### Article information

Source
Electron. Commun. Probab., Volume 14 (2009), paper no. 52, 540-551.

Dates
Accepted: 17 November 2009
First available in Project Euclid: 6 June 2016

https://projecteuclid.org/euclid.ecp/1465234761

Digital Object Identifier
doi:10.1214/ECP.v14-1512

Mathematical Reviews number (MathSciNet)
MR2564488

Zentralblatt MATH identifier
1193.60034

Subjects
Primary: 60F10: Large deviations
Secondary: 60J05: Discrete-time Markov processes on general state spaces

Rights

#### Citation

Liu, Wei; Wu, Liming. Identification of the rate function for large deviations of an irreducible Markov chain. Electron. Commun. Probab. 14 (2009), paper no. 52, 540--551. doi:10.1214/ECP.v14-1512. https://projecteuclid.org/euclid.ecp/1465234761

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