A Note on the Bias and Kemeny's Constant in Markov Reward Processes with an Application to Markov Chain Perturbation
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929453001605120 |
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| author | Ortner, Ronald |
| author_facet | Ortner, Ronald |
| contents | Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny's constant can be interpreted as the translated bias in an MRP with constant reward 1, which offers an intuitive explanation why it is a constant. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_04454 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on the Bias and Kemeny's Constant in Markov Reward Processes with an Application to Markov Chain Perturbation Ortner, Ronald Probability Optimization and Control 60J10, 90C40 Given a unichain Markov reward process (MRP), we provide an explicit expression for the bias values in terms of mean first passage times. This result implies a generalization of known Markov chain perturbation bounds for the stationary distribution to the case where the perturbed chain is not irreducible. It further yields an improved perturbation bound in 1-norm. As a special case, Kemeny's constant can be interpreted as the translated bias in an MRP with constant reward 1, which offers an intuitive explanation why it is a constant. |
| title | A Note on the Bias and Kemeny's Constant in Markov Reward Processes with an Application to Markov Chain Perturbation |
| topic | Probability Optimization and Control 60J10, 90C40 |
| url | https://arxiv.org/abs/2408.04454 |