  Semi-Levy process is an additive process with periodically stationary
increments. In particular, it is a generalization of Levy process. The
dichotomy of recurrence and transience of Levy processes is well known, but
this is not necessarily true for general additive processes. In this paper, we
prove the recurrence and transience dichotomy of semi-Levy processes. For the
proof, we introduce a concept of semi-random walk and discuss its recurrence
and transience properties. An example of semi-Levy process constructed from two
independent Levy processes is investigated. Finally, we prove the laws of large
numbers for semi-Levy processes.
