Time to MRCA for stationary CBI-processes

2013/04/07 by Hongwei Bi, Bi, Hongwei
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1304.2001

15pages. arXiv admin note: text overlap with arXiv:1009.0814 by other authors

arxiv created 2013/04/07 · arxiv updated 2013/04/09

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.

Citations

• Smaller population size at the MRCA time for stationary branching processes

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