Order Statistics Assosiated with Family Size in Branching Processes Allowing Immigration
نویسندگان
چکیده
We study the kth largest value, M (k) n , among the oospring of particles in the nth generation of a branching process with immigration. In particular, M (1) n gives the oospring of the most proliic particle in that generation. Limit theorems for M (k) n and EM (k) n are proved. The results are obtained by combining the extreme value theory methods and known results for the behavior of the population size in branching processes with immigration.
منابع مشابه
Maximum family size in branching processes with state
The number W n of oospring of the most proliic particle in the n-th generation of a simple branching process with state-dependent immigration is studied. Limit theorems for W n and EW n are proved. The results are obtained by combining the methods of 8] with known behavior of the population size in branching processes with state{dependent immigration.
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