Quasistationarity in continuous-time Markov chains where absorption is not certain

Abstract

In a recent paper [4] it was shown that, for an absorbing Markov chain where absorption is not guaranteed, the state probabilities at time t conditional on non-absorption by t generally depend on t. Conditions were derived under which there can be no initial distribution such that the conditional state probabilities are stationary. The purpose of this note is to show that these conditions can be relaxed completely: we prove, once and for all, that there are no circumstances under which a quasistationary distribution can admit a stationary conditional interpretation.