Potentials of skip-free Markov chains

Wendi Li; Jinpeng Liu; Yuanyuan Liu

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arXiv · 2502.00453

Potentials of skip-free Markov chains

Wendi Li·Jinpeng Liu·Yuanyuan Liu

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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.

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Wendi Li, Jinpeng Liu, Yuanyuan Liu. 2025-02-01. Potentials of skip-free Markov chains. https://arxiv.org/abs/2502.00453

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