Bounds for the quasi-stationary distribution of some specialized Markov chains

The quasi-stationary distributions of Markov chains have been investigated by many papers and are known to have considerable practical importance in, e.g., biological, chemical, and applied probability models. However, computation of the quasi-stationary distributions is often nontrivial, which has limited its use in practice despite the usefulness of its own, except for some simple cases. This paper develops some bounds, which are relatively easy to calcualte, for the quasi-stationary distribution of some specialized Markov chains.