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.
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