Transience, Recurrence, and Harris Recurrence

Abstract

Recurrence and transience properties have already been examined in Chapter 6 and 7 for atomic and discrete Markov chains. We revisit these notions for irreducible Markov chains. Some of the properties we have shown for atomic chains extend quite naturally to irreducible chains. This is in particular true of the dichotomy between recurrent and transient chains (compare Theorem 6.2.7 or Theorem 7.1.2 with Theorem 10.1.5 below).