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 co...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.展开更多
基金Acknowledgements The authors would like to thank Professor Yong-Hua Mao for useful discussion. This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11571372, 11501576, 11771452） and the Excellent Young Scientific Research Fund of Hunan Provincial Education Department （Grant No. 15B252）.
文摘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.
