A Certain Class of Foster-Lyapunov Functions and Ergodic Properties for Markov Models
Let be a homogeneous Markov chain with state space , and let be the root of the equation and define . Using or close modifications of as test function in Foster's criteria, conditions for recurrence / geometrically recurrence / transience / ergodicity / null recurrence are developed. Analogous results are obtained for the chains on as well as for continuous time.
As applications, the state-dependent branching processes, allowing immigration at zero, and Ito processes are considered.