Potentials of skip-free Markov chains
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916593589551104 |
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| author | Li, Wendi Liu, Jinpeng Liu, Yuanyuan |
| author_facet | Li, Wendi Liu, Jinpeng Liu, Yuanyuan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00453 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Potentials of skip-free Markov chains Li, Wendi Liu, Jinpeng Liu, Yuanyuan Probability 60J10, 60J45 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. |
| title | Potentials of skip-free Markov chains |
| topic | Probability 60J10, 60J45 |
| url | https://arxiv.org/abs/2502.00453 |