  General characterizations of ergodic Markov chains have been developed in
considerable detail. In this paper, we study the transience for discrete-time
Markov chains on general state spaces, including the geometric transience and
algebraic transience. Criteria are presented through establishing the drift
condition and considering the first return time. As an application, we give
explicit criteria for the random walk on the half line and the skip-free chain
on nonnegative integers.
