树上随机游动的逆问题：网络层析
Inverse problems for random walks on trees: network tomography
摘要：
设$G$是一棵以$r$为根的有限树，并将$G$的内部顶点与一个简单非退化马尔可夫链的转移概率集合相关联.将$G$嵌入到由$G.$的端点粘上长度至少为2的有限线性链构成的图$G^\prime$中，然后$G^\prime$允许不同的边界层，并且与$G$的内部顶点相关的转移概率可以被扩充，从而在$G^\prime.$的顶点上定义一个简单的非退化马尔可夫链$X$。我们证明了$X$的转移概率可以从该MQ恢复对于$G^\prime.$的不同边界层，$X$的首中时和首中位置的联合分布始于根$r$
英文摘要：
Let $G$ be a finite tree with root $r$ and associate to the internal vertices of $G$ a collection of transition probabilities for a simple nondegenerate Markov chain. Embedd $G$ into a graph $G^\prime$ constructed by gluing finite linear chains of length at least 2 to the terminal vertices of $G.$ Then $G^\prime$ admits distinguished boundary layers and the transition probabilities associated to the internal vertices of $G$ can be augmented to define a simple nondegenerate Markov chain $X$ on the vertices of $G^\prime.$ We show that the transition probabilities of $X$ can be recovered from the joint distribution of first hitting time and first hitting place of $X$ started at the root $r$ for the distinguished boundary layers of $G^\prime.$
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