2013/06/01 by Jyy-I Hong
Mathematics · Computer Science · #Stochastic processes and statistical mechanics #Bayesian Methods and Mixture Models #Random Matrices and Applications
paper · pdf · doi:10.1239/jap/1371648962
We consider a continuous-time, single-type, age-dependent Bellman-Harris branching process. We investigate the limit distribution of the point process A(t) = a t,i : 1≤ i ≤ Z(t) , where a t,i is the age of the i th individual alive at time t , 1≤ i ≤ Z(t) , and Z(t) is the population size of individuals alive at time t . Also, if Z(t) ≥ k , k ≥2, is a positive integer, we pick k individuals from those who are alive at time t by simple random sampling without replacement and trace their lines of descent backward in time until they meet for the first time. Let D k(t) be the coalescence time (the death time of the last common ancestor) of these k random chosen individuals. We study the distribution of D k(t) and its limit distribution as t →∞.