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References (3)
-
D. Vere-Jones (1963)
On the spectra of some linear operators associated with queueing systemsZeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, 2
-
D. Kendall (1953)
Stochastic Processes Occurring in the Theory of Queues and their Analysis by the Method of the Imbedded Markov ChainAnnals of Mathematical Statistics, 24
-
D. Vere-Jones (1962)
GEOMETRIC ERGODICITY IN DENUMERABLE MARKOV CHAINSQuarterly Journal of Mathematics, 13
- Publisher
- Springer Journals
- Copyright
- Copyright
- Subject
- Mathematics; Mathematics, general; Algebra; Differential Geometry; Number Theory; Topology; Geometry
- ISSN
- 0025-5858
- eISSN
- 1865-8784
- DOI
- 10.1007/BF02995919
- Publisher site
- See Article on Publisher Site
Abstract
Vere-Jones [5] gave an example, where the geometric ergodicity of a matrixP has a connection with the spectalproperties of an operatorT p. (For the definition ofT p see below [§ 1]). Here it will be proved that one can find for a geometric ergodic stochstic matrixP an operatorT p with the perperty that in the transient case the spectralradius ofT p is smaller 1 and in the recurrent case the spectrum ofT p lies, except a single point at 1, in a circle with radius smaller 1.
Journal
Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg – Springer Journals
Published: Nov 26, 2013