Recurrent sets for transient Lévy processes with bounded kernels (Q1067312)

The author presents two theorems concerning recurrent sets for transient Lévy processes on the real line. The first theorem gives a necessary and sufficient condition for recurrence under the assumption that the continuous process has a bounded kernel. The second one gives a criterion which guarantees a bounded kernel. This result is of independent interest in investigating the behaviour of kernels. Some applications of these results to subordinators in order to construct examples of recurrent sets including a recurrent set with finite Lebesgue measure are presented too.