Abstract: Let be a Markov random walk whose driving chain
with general state space is ergodic with unique stationary distribution
Providing in probability under it is shown that the recurrence set of
forms a closed subgroup of depending on the lattice-type
of The so-called shift function is bounded and appears in that lattice-type
condition. The recurrence set of itself is also given but may look more complicated
depending on The results extend the classical recurrence theorem for random
walks with i.i.d. increments and further sharpen results by Berbee, Dekking and
others on the recurrence behavior of random walks with stationary increments.