Martingale convergence and the stopped branching random walk
Martingale convergence and the stopped branching random walk
复制标题
鞅收敛和停止分支随机游走
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
A. Kyprianou
中科院分区：
文献类型：
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作者：
A. Kyprianou
抽象的。讨论了分枝随机游动中停线的构造，并由此证明了一类由停线序列指标的上鞅的存在性。应用Lyons(1997)和Lyons，Pemantle和Peres(1995)关于大小有偏分枝树的方法，我们建立了停止线与一定的停时之间的关系。因此，我们给出了这些上鞅也是上鞅的条件。在此基础上，我们进一步证明了Biggins(1977a)中的Biggins鞅收敛定理的推广。
Abstract. We discuss the construction of stopping lines in the branching random walk and thus the existence of a class of supermartingales indexed by sequences of stopping lines. Applying a method of Lyons (1997) and Lyons, Pemantle and Peres (1995) concerning size biased branching trees, we establish a relationship between stopping lines and certain stopping times. Consequently we develop conditions under which these supermartingales are also martingales. Further we prove a generalization of Biggins' Martingale Convergence Theorem, Biggins (1977a) within this context.