Quasistationary distributions and ergodic control problems

Quasistationary Distributions for Continuous Timemarkov Chains

Recently, Elmes, Pollett and Walker 2] proposed a deenition 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 (van Doorn 13]) does not hold in the present context. We prove that the state probabilities at time t condi...

Quasistationary Distributions for Level - Dependentquasi - Birth

We consider the problem of identifying the-invariant measures and hence the quasistationary distributions of an absorbing level-dependent quasi-birth-and-death process (QBD); that is, an absorbing Markov chain with a block-tridiagonal transition matrix P. We examine successive lower truncations of P, obtained by removing rows and columns corresponding to levels. The crucial factors in our techn...

Quasistationary Distributions for Continuous-Time Markov Chains

Quasistationary Distributions for Continuous-Time Markov Chains – p.1

Approximations of Quasistationary Distributions for Markov Chains

We consider a simple and widely used method for evaluating quasistationary distributions of continuous time Markov chains. The infinite state space is replaced by a large, but finite approximation, which is used to evaluate a candidate distribution. We give some conditions under which the method works, and describe some important pitfalls. μ-subinvariant measures; conditioned processes; limitin...

Quasistationary Distributions for Level-dependent Quasi-birth-and-death Processes