Quasistationary distributions for continuous time Markov chains when absorption is not certain
1999 ◽
Vol 36
(01)
◽
pp. 268-272
◽
Keyword(s):
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.
1999 ◽
Vol 36
(1)
◽
pp. 268-272
◽
2020 ◽
Vol E103.A
(11)
◽
pp. 1252-1259
2019 ◽
Vol 81
(8)
◽
pp. 3159-3184
◽
2019 ◽
Vol 57
(1)
◽
pp. 192-217
◽
Keyword(s):
2006 ◽
Vol 153
(2)
◽
pp. 259-277
◽