We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.
| Identifer | oai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:5697 |
| Date | January 2012 |
| Creators | Keller, Peter, Roelly, Sylvie, Valleriani, Angelo |
| Publisher | Universität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik |
| Source Sets | Potsdam University |
| Language | English |
| Detected Language | English |
| Type | Preprint |
| Format | application/pdf |
| Rights | http://opus.kobv.de/ubp/doku/urheberrecht.php |
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