Criteria for Geometric and Algebraic Transience for Discrete-Time Markov Chains

We present new criteria for geometric and algebraic transience for discrete-time transient Markov chains on general state spaces, based on the moment of the last exit time, the modified moment of the first return time and the drift condition for the transition kernel. These criteria turn out to be more convenient to use, supplementing and extending conditions introduced by Mao and Song [Stochastic Process. Appl. 124 (2014) 1648-1678]. Several applications are presented including discrete queueing Markov chains, Galton-Watson branching processes, downwardly skip-free chains, unrestricted random walks and autoregressive models of order one.