Unified representation of formulas for single birth processes

doi:10.1007/s11464-014-0381-7

Front. Math. China

2014, Vol. 9

Issue (4) : 761-796 https://doi.org/10.1007/s11464-014-0381-7

RESEARCH ARTICLE

Unified representation of formulas for single birth processes

Mu-Fa CHEN,Yuhui ZHANG(

)

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

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Abstract

Based on a new explicit representation of the solution to the Poisson equation with respect to single birth processes, the unified treatment for various criteria on classical problems (including uniqueness, recurrence, ergodicity, exponential ergodicity, strong ergodicity, as well as extinction probability, etc.) for the processes are presented.

Keywords Single birth process Poisson equation uniqueness recurrence ergodicity moments of return time

Corresponding Author(s): Yuhui ZHANG

Issue Date: 26 August 2014

Cite this article:

Mu-Fa CHEN,Yuhui ZHANG. Unified representation of formulas for single birth processes[J]. Front. Math. China, 2014, 9(4): 761-796.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0381-7
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I4/761

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