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Quasi-stationary distributions Erik A. van Doorna

Summary: Quasi-stationary distributions
Erik A. van Doorna
and Philip K. Pollettb
Department of Applied Mathematics, University of Twente
P.O. Box 217, 7500 AE Enschede, The Netherlands
E-mail: e.a.vandoorn@utwente.nl
Department of Mathematics, The University of Queensland
Qld 4072, Australia
E-mail: pkp@maths.uq.edu.au
June 17, 2011
Abstract. This paper contains a survey of results related to quasi-stationary
distributions, which arise in the setting of stochastic dynamical systems that
eventually evanesce, and which may be useful in describing the long-term be-
haviour of such systems before evanescence. We are concerned mainly with
continuous-time Markov chains over a finite or countably infinite state space,
since these processes most often arise in applications, but will make reference
to results for other processes where appropriate. Next to giving an historical
account of the subject, we review the most important results on the existence


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering