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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

Postal Subscription Code 80-964

2018 Impact Factor: 0.565

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Front. Math. China    2014, Vol. 9 Issue (2) : 239-260    https://doi.org/10.1007/s11464-014-0354-x
RESEARCH ARTICLE
Time to most recent common ancestor for stationary continuous state branching processes with immigration
BI Hongwei1,()
School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China
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Abstract

Motivated by sample path decomposition of the stationary continuous state branching process with immigration, a general population model is considered using the idea of immortal individual. We compute the joint distribution of the random variables: the time to the most recent common ancestor (MRCA), the size of the current population, and the size of the population just before MRCA. We obtain the bottleneck effect as well. The distribution of the number of the oldest families is also established. These generalize the results obtained by Y. T. Chen and J. F. Delmas.
Keywords Continuous state branching process with immigration (CBIprocesses)      most recent common ancestor (MRCA)      measured rooted real tree      decomposition     
Corresponding Author(s): BI Hongwei   
Issue Date: 16 May 2014
 Cite this article:   
BI Hongwei. Time to most recent common ancestor for stationary continuous state branching processes with immigration[J]. Front. Math. China, 2014, 9(2): 239-260.
 URL:  
https://academic.hep.com.cn/fmc/EN/10.1007/s11464-014-0354-x
https://academic.hep.com.cn/fmc/EN/Y2014/V9/I2/239
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