Journal of Applied Probability

Additive functionals for discrete-time Markov chains with applications to birth-death processes

Yuanyuan Liu

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In this paper we are interested in bounding or calculating the additive functionals of the first return time on a set for discrete-time Markov chains on a countable state space, which is motivated by investigating ergodic theory and central limit theorems. To do so, we introduce the theory of the minimal nonnegative solution. This theory combined with some other techniques is proved useful for investigating the additive functionals. This method is used to study the functionals for discrete-time birth-death processes, and the polynomial convergence and a central limit theorem are derived.

Article information

J. Appl. Probab., Volume 48, Number 4 (2011), 925-937.

First available in Project Euclid: 16 December 2011

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Zentralblatt MATH identifier

Primary: 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 60J55: Local time and additive functionals

Additive functional birth-death process ergodicity central limit theorem


Liu, Yuanyuan. Additive functionals for discrete-time Markov chains with applications to birth-death processes. J. Appl. Probab. 48 (2011), no. 4, 925--937. doi:10.1239/jap/1324046010.

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