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.

Recently, Elmes et al. (see [2]) proposed a definition of a quasistationary distribution to accommodate absorbing Markov chains for which absorption occurs with probability less than 1. We will show that the probabilistic interpretation pertaining to cases where absorption is certain (see [13]) does not hold in the present context. We prove that the state probabilities at time t conditional on absorption taking place after t, generally depend on t. Conditions are derived under which there is no initial distribution such that the conditional state probabilities are stationary.