Quasistationary distributions for reducible absorbing Markov chains in discrete time
Pollett, P.K. and Doorn, E.A. van (2008) Quasistationary distributions for reducible absorbing Markov chains in discrete time. [Report]

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Abstract:  We consider discretetime Markov chains with one coffin state and a finite set of transient states, and are interested in the limiting behaviour of such a chain as time conditional on survival up to . It is known that, when is irreducible, the limiting conditional distribution of the chain equals the (unique) quasistationary distribution of the chain, while the latter is the (unique) invariant distribution for the onestep transition probability matrix of the (sub)Markov chain on being the PerronFrobenius eigenvalue of this matrix. Addressing similar issues in a setting in which may be reducible, we identify all quasistationary distributions and obtain a necessary and sufficient condition for one of them to be the unique invariant distribution. We also reveal conditions under which the limiting conditional distribution equals the invariant distribution if it is unique. We conclude with some examples. 
Item Type:  Report 
Faculty:  Electrical Engineering, Mathematics and Computer Science (EEMCS) 
Research Group:  
Link to this item:  http://purl.utwente.nl/publications/65084 
Publisher URL:  http://www.math.utwente.nl/publications 
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