Kemeny's Constant for Markov Processes
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908828341108736 |
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| author | Fitzsimmons, P. J. |
| author_facet | Fitzsimmons, P. J. |
| contents | The mean time taken by an irreducible Markov chain on a finite state space to hit a target chosen at random according to the stationary distribution does not depend on the initial state of the chain. This mean time is known as Kemeny's constant. I present a new approach, based on time reversal and a mean occupation time formula.
The method is used to prove an analogous result for continuous-time Markov processes. We also present a second approach, based on work of N.~Eisenbaum and H.~Kaspi, when all states are regular.
Examples are provided. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19273 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kemeny's Constant for Markov Processes Fitzsimmons, P. J. Probability Primary 60J10, Secondary 60J25, 60J45, 60J55 The mean time taken by an irreducible Markov chain on a finite state space to hit a target chosen at random according to the stationary distribution does not depend on the initial state of the chain. This mean time is known as Kemeny's constant. I present a new approach, based on time reversal and a mean occupation time formula. The method is used to prove an analogous result for continuous-time Markov processes. We also present a second approach, based on work of N.~Eisenbaum and H.~Kaspi, when all states are regular. Examples are provided. |
| title | Kemeny's Constant for Markov Processes |
| topic | Probability Primary 60J10, Secondary 60J25, 60J45, 60J55 |
| url | https://arxiv.org/abs/2509.19273 |