首中时和交错特征值：一种使用交织的随机方法
Hitting times and interlacing eigenvalues: a stochastic approach using intertwinings
摘要：
我们开发了一个系统的矩阵分析方法，基于交织的马尔可夫半群，证明定理的命中时间分布有限状态马尔可夫链-一种方法，（有时）加深理解的定理，提供相应的样本路径的样本路径随机结构。我们采用我们的方法给新的证明和结构的两个定理，由于马克布朗，定理给出两个完全不同的表示有限状态马尔可夫链的击中时间分布开始平稳。两个定理之一的证明和相应的构造阐明了有边对称矩阵的击中时间分布和交错特征值定理之间的有趣联系。
英文摘要：
We develop a systematic matrix-analytic approach, based on intertwinings of Markov semigroups, for proving theorems about hitting-time distributions for finite-state Markov chains -- an approach that (sometimes) deepens understanding of the theorems by providing corresponding sample-path-by-sample-path stochastic constructions. We employ our approach to give new proofs and constructions for two theorems due to Mark Brown, theorems giving two quite different representations of hitting-time distributions for finite-state Markov chains started in stationarity. The proof, and corresponding construction, for one of the two theorems elucidates an intriguing connection between hitting-time distributions and the interlacing eigenvalues theorem for bordered symmetric matrices.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
