Integral-type functionals of first hitting times for continuous-time Markov chains

doi:10.1007/s11464-018-0700-5

Front. Math. China

2018, Vol. 13

Issue (3) : 619-632 https://doi.org/10.1007/s11464-018-0700-5

RESEARCH ARTICLE

Integral-type functionals of first hitting times for continuous-time Markov chains

Yuanyuan LIU¹(

), Yanhong SONG²

¹. School of Mathematics and Statistics, Central South University, Changsha 410083, China
². School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

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Abstract

We investigate integral-type functionals of the first hitting times for continuous-time Markov chains. Recursive formulas and drift conditions for calculating or bounding integral-type functionals are obtained. The connection between the subexponential integral-type functionals and the subexponential ergodicity is established. Moreover, these results are applied to the birth-death processes. Polynomial integral-type functionals and polynomial ergodicity are studied, and a sufficient criterion for a central limit theorem is also presented.

Keywords Integral-type functional continuous-time Markov chain (CTMC) subexponential ergodicity birth-death process central limit theorem (CLT)

Corresponding Author(s): Yuanyuan LIU

Issue Date: 11 June 2018

Cite this article:

Yuanyuan LIU,Yanhong SONG. Integral-type functionals of first hitting times for continuous-time Markov chains[J]. Front. Math. China, 2018, 13(3): 619-632.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0700-5
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I3/619

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