General drift 条件 for algebraic ergodicity of discrete-time Markov chains

The classical drift 条件 for the stochastic stability of discrete-time Markov chains solely involve the one-step transition kernel, and the test functions are dependent only on one state of Markov chains. However, for the stochastic stability of some complex high-dimensional models, it may be impractical to analyse one-step drift 条件. In this paper, we consider three types of more general drift 条件 for algebraic ergodicity of discrete-time Markov chains on general state spaces, including fixed state-dependent time 条件, random state-dependent time 条件, and stopping time 条件. As an application, we study algebraic ergodicity for invasion/defense models.