English

Upward and Downward Runs on Partially Ordered Sets

Probability 2010-04-08 v2

Abstract

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.

Keywords

Cite

@article{arxiv.0810.2289,
  title  = {Upward and Downward Runs on Partially Ordered Sets},
  author = {Kyle Siegrist},
  journal= {arXiv preprint arXiv:0810.2289},
  year   = {2010}
}

Comments

13 pages

R2 v1 2026-06-21T11:30:15.514Z