偏序集上的向上和向下映射
Upward and Downward Runs on Partially Ordered Sets
摘要：
本文研究偏序集上的马尔可夫链，推广了可靠性理论中的成功运行链和剩余寿命链。我们发现条件的复发和瞬态，并给出简单的表达式不变的分布。我们研究了一些特殊的情况，包括有根树，一致偏序集，偏序集与正半群。
英文摘要：
We consider Markov chains on partially ordered sets that generalize the success-runs and remaining life chains in reliability theory. We find conditions for recurrence and transience and give simple expressions for the invariant distributions. We study a number of special cases, including rooted trees, uniform posets, and posets associated with positive semigroups.
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。
