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Recurrent sets for transient Lévy processes with bounded kernels. (English) Zbl 0579.60073

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.
Reviewer: Z.Rychlik

MSC:

60J99 Markov processes
60G17 Sample path properties
60J45 Probabilistic potential theory
60K05 Renewal theory
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