English

Potentials of skip-free Markov chains

Probability 2025-02-04 v1

Abstract

Potential theory has important applications in various fields such as physics, finance, and biology. In this paper, we investigate the potentials of two classic types of discrete-time skip-free Markov chains: upward skip-free and downward skip-free Markov chains. The key to deriving these potentials lies in the use of truncation approximation techniques. The results are then applied to GI/M/1 queues and M/G/1 queues, and further extended to continuous-time skip-free Markov chains.

Keywords

Cite

@article{arxiv.2502.00453,
  title  = {Potentials of skip-free Markov chains},
  author = {Wendi Li and Jinpeng Liu and Yuanyuan Liu},
  journal= {arXiv preprint arXiv:2502.00453},
  year   = {2025}
}

Comments

19 pages,2 figures

R2 v1 2026-06-28T21:28:59.747Z