Extinction Probabilities of Branching Processes with Countably Infinitely Many Types
Extinction Probabilities of Branching Processes with Countably Infinitely Many Types
复制标题
可数无穷多类型分支过程的灭绝概率
DOI：
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发表时间：
2012
影响因子：
1.2
通讯作者：
G. Nguyen
中科院分区：
文献类型：
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作者：
S. Hautphenne;G. Latouche;G. Nguyen
给出了计算可数无穷多个Galton-Watson过程的全局灭绝概率向量和部分灭绝概率向量的两种迭代方法。这些方法的概率解释涉及有限类型集的截断Galton-Watson过程和修正的子代母函数。此外，我们还讨论了平均子代矩阵的收敛范数与灭绝准则之间的关系。最后，我们给出了一个种群灭绝的充分条件，即使种群规模平均呈爆炸式增长，这在有限个类型的分枝过程中是不可能的。最后，我们用一些数值例子说明了我们的算法方法。
We present two iterative methods for computing the global and partial extinction probability vectors for Galton-Watson processes with countably infinitely many types. The probabilistic interpretation of these methods involves truncated Galton-Watson processes with finite sets of types and modified progeny generating functions. In addition, we discuss the connection of the convergence norm of the mean progeny matrix with extinction criteria. Finally, we give a sufficient condition for a population to become extinct almost surely even though its population size explodes on the average, which is impossible in a branching process with finitely many types. We conclude with some numerical illustrations for our algorithmic methods.