Fine Irreducibility Of The Levy Process By Harris Irreducibility

In the paper, we talk about the problems about fine irreducible and harris irre-ducible. Assume the process is LSC, we give the condition which can result in fine irreducible by talking about generating triplets and moment generating function:In the same time, I also give a condition, which can promise LSC. For the harris irre-ducible. I also give a condition, when this condition is satisfied, harris irreducible is equal to fine irreducible.