@book{413c4dc2e306405abd349a5f147a4983,

title = "Quasi-stationary distributions for reducible absorbing Markov chains in discrete time",

abstract = "We consider discrete-time Markov chains with one coffin state and a finite set $S$ of transient states, and are interested in the limiting behaviour of such a chain as time $n \to \infty,$ conditional on survival up to $n$. It is known that, when $S$ is irreducible, the limiting conditional distribution of the chain equals the (unique) quasi-stationary distribution of the chain, while the latter is the (unique) $\rho$-invariant distribution for the one-step transition probability matrix of the (sub)Markov chain on $S,$ $\rho$ being the Perron-Frobenius eigenvalue of this matrix. Addressing similar issues in a setting in which $S$ may be reducible, we identify all quasi-stationary distributions and obtain a necessary and sufficient condition for one of them to be the unique $\rho$-invariant distribution. We also reveal conditions under which the limiting conditional distribution equals the $\rho$-invariant distribution if it is unique. We conclude with some examples.",

keywords = "limiting conditional distribution, IR-65084, Absorbing Markov chain, MSC-60J10, EWI-14022, survival-time distribution, MSC-15A18, rho-invariant distribution, METIS-252095",

author = "P.K. Pollett and {van Doorn}, {Erik A.}",

note = "http://eprints.ewi.utwente.nl/14022 ",

year = "2008",

month = nov,

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

publisher = "University of Twente, Department of Applied Mathematics",

number = "10/1885",

}