Inverse Problems for Ergodicity of Markov Chains

Here is the Journal Page. An early version is posted here on arXiv.

This work is in fact my Master degree thesis in 2018 at Beijing Normal University. The thesis version is available via Beijing Normal University library. It could also be downloaded here.

Abstract

For continuous-time Markov chains, we provide criteria for non-ergodicity, non-algebraic ergodicity, non-exponential ergodicity, and non-strong ergodicity. For discrete-time Markov chains, criteria for non-ergodicity, non-algebraic ergodicity, and non-strong ergodicity are given. Our criteria are in terms of the existence of solutions to inequalities involving the $Q$-matrix (or transition matrix $P$ in time-discrete case) of the chain. Meanwhile, these practical criteria are applied to some examples, including a special class of single birth processes and several multi-dimensional models.