In a branching process having X0 = 1 and >1, prove that 0 is the smallest positive
Question:
In a branching process having X0 = 1 and μ>1, prove that π0 is the smallest positive number satisfying Eq. (4.20).
Hint: Let π be any solution of π =∞
j=0 πjPj . Show by mathematical induction that π P{Xn = 0} for all n, and let n→∞. In using the induction argue that
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