Calculating Bounds on Expected Return and First Passage Times in Finite-State Imprecise Birth-Death Chains

We provide simple methods for computing exact bounds on expected return and first passage times in finite-state birth-death chains, when the transition probabilities are imprecise, in the sense that they are only known to belong to convex closed sets of probability mass functions.These so-called imprecise birthdeath chains are special types of time-homogeneous imprecise Markov chains.We also present numerical results and discuss the special case where the local models are linear-vacuous mixtures, for which our methods simplify even more.