Frontiers of Mathematics in China >
High order moments of first hitting times for single death processes
Received date: 22 Apr 2019
Accepted date: 19 Jul 2019
Published date: 15 Oct 2019
Copyright
We present an explicit and recursive representation for high order moments of the first hitting times of single death processes. Based on that, some necessary or sufficient conditions of exponential ergodicity as well as a criterion on-ergodicity are obtained for single death processes, respectively.
Yuhui ZHANG , Xiaofeng ZHOU . High order moments of first hitting times for single death processes[J]. Frontiers of Mathematics in China, 2019 , 14(5) : 1037 -1061 . DOI: 10.1007/s11464-019-0780-x
1 |
Asmussen S, Hering H. Branching Processes. Basel: Birkhauser, 1983
|
2 |
Athreya K B, Ney P E. Branching Processes. Berlin: Springer, 1972
|
3 |
Chen A Y, Pollett P, Zhang H J, Cairns B. Uniqueness criteria for continuous-time Markov chains with general transition structure. Adv Appl Probab, 2005, 37(4): 1056–1074
|
4 |
Chen M F. Explicit bounds of the first eigenvalue. Sci China Math, 2000, 43(10): 1051–1059
|
5 |
Chen M F. From Markov Chains to Non-Equilibrium Particle Systems. 2nd ed. Singapore: World Scientific, 2004
|
6 |
Mao Y H. Ergodic degrees for continuous-time Markov chains. Sci China Math, 2004, 47(2): 161–174
|
7 |
Wang L D, Zhang Y H. Criteria for zero-exit (-entrance) of single-birth (-death) Q-matrices. Acta Math Sinica (Chin Ser), 2014, 57(4): 681–692 (in Chinese)
|
8 |
Wang Z K. Introduction to Stochastic Processes, Vol 2. Beijing: Beijing Normal Univ Press, 1996 (in Chinese)
|
9 |
Zhang Y H. Criteria on ergodicity and strong ergodicity of single death processes. Front Math China, 2018, 13(5): 1215–1243
|
10 |
Zhang Y H. Moments of first hitting times for birth-death processes on trees. Front Math China, 2019, 14(4): 833–854
|
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