Abstract
We investigate general properties of branching processes with killing. These are Galton- Watson processes having the possibility of being terminated with a probability depending on the size of the current generation. A special case has arisen in problems of detecting particular genotypes, where the probability of termination is 1− α j when the current generation number is j. We show that the analysis of this case can be carried out using known results about the total progeny in branching processes.
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