On time duality for Markov Chains
- For an irreducible continuous time Markov chain, we derive the distribution of the first passage time from a given state i to another given state j and the reversed passage time from j to i, each under the condition of no return to the starting point. When these two distributions are identical, we say that i and j are in time duality. We introduce a new condition called permuted balance that generalizes the concept of reversibility and provides sufficient criteria, based on the structure of the transition graph of the Markov chain. Illustrative examples are provided.
| Author details: | Peter Keller, Sylvie RoellyGND, Angelo VallerianiORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1080/15326349.2014.969736 |
| ISSN: | 1532-6349 |
| ISSN: | 1532-4214 |
| Title of parent work (English): | Stochastic models |
| Publisher: | Taylor & Francis Group |
| Place of publishing: | Philadelphia |
| Publication type: | Article |
| Language: | English |
| Year of first publication: | 2015 |
| Publication year: | 2015 |
| Release date: | 2017/03/27 |
| Tag: | Detailed balance; First passage time; Markov chain; Permuted balance; Reversibility; Time duality |
| Volume: | 31 |
| Issue: | 1 |
| Number of pages: | 21 |
| First page: | 98 |
| Last Page: | 118 |
| Funding institution: | National Philanthropic Trust (FQEB) [RFP-12-18] |
| Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik |
| Peer review: | Referiert |
