MATH 632 Final: 2007 Math 632 - Seppalainen - Spring Final Exam
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Instructions: show calculations and give concise justi cations for full credit. Points add up to 200: born again branching process. Let {pk}0 k< be the o spring distribution of a branching process. Assume 0 < p0 < 1 so that interesting behavior is possible and let m be the mean of the o spring distribution. Let the process begin with one progenitor, and let xn be the population size of the nth generation with x0 = 1. The galton-watson branching process we studied in chapter 1 was ab- sorbed at zero if it ever dies out. Now we give the process a chance to come to life again after extinction. Take another parameter 0 < < 1. Explain. (c) (20 pts) let t be the total amount of time the chain xn spends in state 0, throughout its entire evolution. Compute the mean of t . (the answer should contain as a parameter the extinction probability of the.
