Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
Limit Theorems for Weakly Subcritical Branching Processes in Random Environment
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DOI：
10.1007/s10959-010-0331-6
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发表时间：
2010-01
影响因子：
0.8
通讯作者：
V. Afanasyev;C. Böinghoff;G. Kersting;V. Vatutin
中科院分区：
文献类型：
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作者：
V. Afanasyev;C. Böinghoff;G. Kersting;V. Vatutin
对于随机环境中的分支过程，假设个体的后代分布是以随机方式变化的，独立于一代到另一代。有趣的是，有一种可能性是，这个过程可能同时是亚临界的，并且在不灭绝的条件下，是“超临界的”。本文考虑了这一所谓的弱亚临界情形。我们研究了非灭绝条件下种群的渐近生存概率和种群规模。证明了一个泛函极限定理，使条件超临界变得明显。一个主要的工具是条件随机游动的一类新的泛函极限定理。
For a branching process in random environment, it is assumed that the offspring distribution of the individuals varies in a random fashion, independently from one generation to the other. Interestingly there is the possibility that the process may at the same time be subcritical and, conditioned on nonextinction, “supercritical.” This so-called weakly subcritical case is considered in this paper. We study the asymptotic survival probability and the size of the population conditioned on nonextinction. Also a functional limit theorem is proved, which makes the conditional supercriticality manifest. A main tool is a new type of functional limit theorems for conditional random walks.