无宽 sense 再生结构的 Harris 常返连续时间马尔可夫过程
A Harris recurrent continuous-time Markov process without wide-sense regenerative structure
浏览论文内容
中文总结 AI 辅助
本文构造了一个不具备宽 sense 再生结构的 Harris 常返连续时间马尔可夫过程，对相关开放问题给出否定答案，其构造关键在于利用有理数上线性无关的 Cantor 集。
中文摘要 AI 辅助
离散时间的 Harris 常返马尔可夫链会自动呈现宽 sense 再生结构，而本文构造了一个不具备宽 sense 再生结构的 Harris 常返连续时间马尔可夫过程，从而对 20 世纪 90 年代首次提出、后由 Glynn（2011）提出的开放问题给出否定答案。该反例具有如下刚性性质：每个与该时刻观测状态独立的几乎必然有限随机时间必为几乎必然常数。在构造中，有理数上线性无关的 Cantor 集起到关键作用，将日历时间转化为已遍历路径的代数记录。
英文摘要
While Harris recurrent Markov chains (in discrete time) automatically exhibit wide-sense regenerative structure, we construct a Harris recurrent Markov process (in continuous time) that is not wide-sense regenerative, thereby giving a negative answer to the open problem first raised in the 1990s and later posed in Glynn(2011). The counterexample exhibits the following rigidity property: every almost surely finite random time that is independent of the state observed at that time must be almost surely constant. A Cantor set linearly independent over the rationals plays a key role in the construction, turning calendar time into an algebraic record of the path already traversed.
