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NCTS Probability Seminar
 
10:30 - 12:00, March 27, 2017 (Monday)
070116, Zhi Xi Building, NCCU
(政大應數系志希樓 070116)
The Coalescence Problem in Branching Processes and its Applications
Jyy-I Hong (National Sun Yat-sen University)

Abstract

A branching process is a mathematical model which has been com- monly used to describe the evolution of a population in various re- search fields such as genealogy, physics, ecology, epidemiology, fi- nance, etc. One way to investigate the population is to look forward to its future. But, when a population grows so old, it is always in- teresting to know what happened to it in the past. The coalescence problem provides a way to understand the structure of the popula- tion and the ancestry of the individuals in it.

Here, we will consider branching processes with different settings and, in each process, We pick two individuals from those who are alive at the current time by simple random sampling without re- placement and trace their lines of descent backward in time till they meet for the first time. We call the common ancestor of these chosen individuals at the coalescent time their most recent common ances- tor. The coalescence problem is to investigate the limit behaviors of some characteristics of this most recent common ancestor such as its death time and its generation number. Moreover, we will also ap- ply the results from the coalescence problem to branching random walks.



 

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