布朗游标内的样本谱系
Sample genealogies within a Brownian excursion
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中文总结 AI 辅助
本文利用伊藤游标理论推导布朗游标条件化上升至水平1时，由k个独立同分布交点定义的区间内最小值的联合分布，进而得到Aldous连续随机树中k个粒子样本的合并时间联合分布，与关键Galton-Watson树的极限采样结果一致。
中文摘要 AI 辅助
在本文中，我们应用伊藤游标理论来寻找布朗游标在条件化上升至水平$1$时，由$k$个独立同分布（i.i.d.）的游标与水平$a \in (0,1]$的交点所定义的区间内最小值的联合分布。这种方法提供了一种直观的方式，来寻找Aldous高度为$1$的连续随机树中在时间$a$存活的$k$个粒子的i.i.d.样本的合并时间的联合分布。这可以被视为对条件化存活长时间的关键Galton-Watson树的“极限采样”，与文献[4]和[5]中获得的某些特殊情况一致，而后者考虑的是来自关键Galton-Watson树的“采样极限”。
英文摘要
In this article, we apply Itô's excursion theory to find the joint law of minima of a Brownian excursion conditioned to go above level $1$ over the intervals defined by $k$ independent identically distributed (i.i.d.) points of intersection of the excursion with level $a \in (0,1]$. This approach offers an intuitive way to find the joint law of coalescent times of an i.i.d. sample of k particles alive at time $a$ in Aldous' continuum random tree of height $1$. This can be thought of as ``sampling of the limit" of critical Galton-Watson trees conditioned to survive a large time, agreeing with some special cases obtained in [4] and [5] which instead consider ``the limit of sampling" from critical Galton-Watson trees.
