On time duality for quasi-birth-and-death processes

Keller, Peter; Roelly, Sylvie; Valleriani, Angelo

On time duality for quasi-birth-and-death processes

Peter Keller, Sylvie Roelly, Angelo Valleriani

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.

Metadaten
Author details:	Peter Keller, Sylvie Roelly GND, Angelo Valleriani ORCiD GND
URN:	urn:nbn:de:kobv:517-opus-56973
Publication series (Volume number):	Preprints des Instituts für Mathematik der Universität Potsdam (1 (2012) 4)
Publication type:	Preprint
Language:	English
Publication year:	2012
Publishing institution:	Universität Potsdam
Release date:	2012/01/06
Tag:	absorbing boundary; continuous time Markov chain; hitting times; time duality
Organizational units:	Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:	5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J27 Continuous-time Markov processes on discrete state spaces
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Jxx Markov processes / 60J28 Applications of continuous-time Markov processes on discrete state spaces
	60-XX PROBABILITY THEORY AND STOCHASTIC PROCESSES (For additional applications, see 11Kxx, 62-XX, 90-XX, 91-XX, 92-XX, 93-XX, 94-XX) / 60Kxx Special processes / 60K40 Other physical applications of random processes
Collection(s):	Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
License (German):	Keine öffentliche Lizenz: Unter Urheberrechtsschutz
External remark:	RVK-Klassifikation: SI 990 , SK 820

On time duality for quasi-birth-and-death processes

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