High order moments of first hitting times for single death processes

doi:10.1007/s11464-019-0780-x

Front. Math. China

2019, Vol. 14

Issue (5) : 1037-1061 https://doi.org/10.1007/s11464-019-0780-x

RESEARCH ARTICLE

High order moments of first hitting times for single death processes

Yuhui ZHANG(

), Xiaofeng ZHOU

School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Download: PDF(321 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

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 $ℓ$ -ergodicity are obtained for single death processes, respectively.

Keywords Single death process moment of the first hitting time exponential ergodocity

Corresponding Author(s): Yuhui ZHANG

Issue Date: 22 November 2019

Cite this article:

Yuhui ZHANG,Xiaofeng ZHOU. High order moments of first hitting times for single death processes[J]. Front. Math. China, 2019, 14(5): 1037-1061.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-019-0780-x
https://academic.hep.com.cn/fmc/EN/Y2019/V14/I5/1037

1	S Asmussen, H Hering. Branching Processes. Basel: Birkhauser, 1983 https://doi.org/10.1007/978-1-4615-8155-0
2	K B Athreya, P E Ney. Branching Processes. Berlin: Springer, 1972 https://doi.org/10.1007/978-3-642-65371-1
3	A Y Chen, P Pollett, H J Zhang, B Cairns. Uniqueness criteria for continuous-time Markov chains with general transition structure. Adv Appl Probab, 2005, 37(4): 1056–1074 https://doi.org/10.1239/aap/1134587753
4	M F Chen. Explicit bounds of the first eigenvalue. Sci China Math, 2000, 43(10): 1051–1059 https://doi.org/10.1007/BF02898239
5	M F Chen. From Markov Chains to Non-Equilibrium Particle Systems. 2nd ed. Singapore: World Scientific, 2004 https://doi.org/10.1142/5513
6	Y H Mao. Ergodic degrees for continuous-time Markov chains. Sci China Math, 2004, 47(2): 161–174 https://doi.org/10.1360/02ys0306
7	L D Wang, Y H Zhang. Criteria for zero-exit (-entrance) of single-birth (-death) Q-matrices. Acta Math Sinica (Chin Ser), 2014, 57(4): 681–692 (in Chinese)
8	Z K Wang. Introduction to Stochastic Processes, Vol 2. Beijing: Beijing Normal Univ Press, 1996 (in Chinese)
9	Y H Zhang. Criteria on ergodicity and strong ergodicity of single death processes. Front Math China, 2018, 13(5): 1215–1243 https://doi.org/10.1007/s11464-018-0722-z
10	Y H Zhang. Moments of first hitting times for birth-death processes on trees. Front Math China, 2019, 14(4): 833–854 https://doi.org/10.1007/s11464-019-0784-6

[1]	Jing WANG, Yuhui ZHANG. Moments of integral-type downward functionals for single death processes[J]. Front. Math. China, 2020, 15(4): 749-768.
[2]	Yuhui ZHANG. Criteria on ergodicity and strong ergodicity of single death processes[J]. Front. Math. China, 2018, 13(5): 1215-1243.

Viewed

Full text

Abstract

Cited

Shared

Discussed