For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been f...For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been found.展开更多
Of repeated hits and repeated explosions after first explosion for a birth and death process with explosion some properties are investigated. The properties of repeated hits after first explosion may be expressed by t...Of repeated hits and repeated explosions after first explosion for a birth and death process with explosion some properties are investigated. The properties of repeated hits after first explosion may be expressed by the properties of the first hit after the first explosion.展开更多
The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which dep...The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.展开更多
For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal ...For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.展开更多
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
文摘For a birth and death processX=|X(t),t <σ| with explosion and lifespanu distributions and joint distributions of first hitting time and first hitting location after explosion of setB n = |0,1,...,n| ,n have been found.
基金Project supported by the National Natural Science Foundation of China (Grant No. 19761028)the Centre of Researching Mathematics and Forstering Higher Talent, the Ministry of Education of China
文摘Of repeated hits and repeated explosions after first explosion for a birth and death process with explosion some properties are investigated. The properties of repeated hits after first explosion may be expressed by the properties of the first hit after the first explosion.
基金Acknowledgements This work was supported in part by 985 Project, 973 Project （No. 2011CB808000）, the National Natural Science Foundation of China （Grant No. 11131003）, the Specialized Research Fund for the Doctoral Program of Higher Education （No. 20100003110005）, and the Fundamental Research Funds for the Central Universities.
文摘The criteria on separation cutoff for birth and death chains were obtained by Diaconis and Saloff-Coste in 2006. These criteria are involving all eigenvalues. In this paper, we obtain the explicit criterion, which depends only on the birth and death rates. Furthermore, we present two ways to estimate moments of the fastest strong stationary time and then give another but equivalent criterion explicitly.
基金Supported by the National Natural Science Foundation of China(Grant Nos.11501531,11701265,11771047)。
文摘For the birth–death Q-matrix with regular boundary,its minimal process and its maximal process are closely related.In this paper,we obtain the uniform decay rate and the quasi-stationary distribution for the minimal process.And via the construction theory,we mainly derive the eigentime identity and the distribution of the fastest strong stationary time(FSST)for the maximal process.
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.
