Frontiers of Mathematics in China >

2014 , Vol. 9 >Issue 4: 761 - 796

DOI: https://doi.org/10.1007/s11464-014-0381-7

RESEARCH ARTICLE

Unified representation of formulas for single birth processes

  • Mu-Fa CHEN ,
  • Yuhui ZHANG
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  • School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China

Received date: 05 Mar 2014

Accepted date: 02 Apr 2014

Published date: 20 Aug 2014

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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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.

Key words： Single birth process; Poisson equation; uniqueness; recurrence; ergodicity; moments of return time

Cite this article

Mu-Fa CHEN , Yuhui ZHANG . Unified representation of formulas for single birth processes[J]. Frontiers of Mathematics in China, 2014 , 9(4) : 761 -796 . DOI: 10.1007/s11464-014-0381-7

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