Limit theorems for the minimal position in a branching random walk with independent logconcave displacements
Limit theorems for the minimal position in a branching random walk with independent logconcave displacements
复制标题
具有独立对数凹位移的分支随机游走中最小位置的极限定理
DOI：
10.1239/aap/1013540028
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发表时间：
2000
影响因子：
1.2
通讯作者：
Markus Bachmann
中科院分区：
文献类型：
--
作者：
Markus Bachmann
考虑一个分支随机游动，其中每个粒子都有一个随机数（一个或多个）的后代粒子，这些后代粒子根据对数凹密度相互独立地移动。在适当的附加假设下，我们得到了如下结果：第n代的极小值位置经α分位数调整后，弱收敛于一个非退化的极限分布.也存在一个“条件限制”的调整后的最小位置，它有一个（Gumbel）的极值分布延迟一个随机的时滞。因此，无条件极限分布是极值分布的混合。
Consider a branching random walk in which each particle has a random number (one or more) of offspring particles that are displaced independently of each other according to a logconcave density. Under mild additional assumptions, we obtain the following results: the minimal position in the nth generation, adjusted by its α-quantile, converges weakly to a non-degenerate limiting distribution. There also exists a ‘conditional limit’ of the adjusted minimal position, which has a (Gumbel) extreme value distribution delayed by a random time-lag. Consequently, the unconditional limiting distribution is a mixture of extreme value distributions.