@book{7063b001d31045eebcf799d9c2e6eb37,

title = "Survival in a quasi-death process",

abstract = "We consider a Markov chain in continuous time with an absorbing coffin state and a finite set $S$ of transient states. When $S$ is irreducible the limiting distribution of the chain as $t \to\infty,$ conditional on survival up to time $t,$ is known to equal the (unique) quasi-stationary distribution of the chain. We address the problem of generalizing this result to a setting in which $S$ may be reducible, and obtain a complete solution if the eigenvalue with maximal real part of the generator of the (sub)Markov chain on $S$ has multiplicity one. The result is applied to pure death processes and, more generally, to quasi-death processes.",

keywords = "limiting conditional distribution, MSC-60J27, Absorbing Markov chain, Quasi-stationary distribution, EWI-8237, survival-time distribution, death process, METIS-241734, IR-66636",

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

year = "2007",

month = jan,

language = "Undefined",

series = "Memorandum / Department of Applied Mathematics",

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

number = "1/1815",

}