A Markov chain associated with the minimal quasi-stationary distribution of birth–death chains

Servet Martínez, Maria Eulália Vares
1995 Journal of Applied Probability  
We show that if the limiting conditional distribution for an absorbed birth–death chain exists, then the chain conditioned to non-absorption converges to a Markov chain with transition probabilities given by the matrix associated with the minimal quasi-stationary distribution.
doi:10.2307/3214918 fatcat:uqx5efddcrfbnex4zkrs74uhcq