Upward and Downward Runs on Partially Ordered Sets
Kyle T. Siegrist · arXiv (Cornell University) · 2008
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.