Open Access
November, 1985 Recurrent Sets for Transient Levy Processes with Bounded Kernels
Steven J. Janke
Ann. Probab. 13(4): 1204-1218 (November, 1985). DOI: 10.1214/aop/1176992805


In the study of recurrent sets for transient Levy processes on the real line, we present two main results. As long as the process has a "well-behaved" (bounded in a particular way) kernel, a set is recurrent for the process if and only if the sum of the capacities of pieces of the set is infinite. In the second result, we show that a simple condition on the Levy measure guarantees that the process has a "well-behaved" kernel. Finally, the results are applied to subordinators in order to construct examples of recurrent sets including a recurrent set with finite Lebesgue measure.


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Steven J. Janke. "Recurrent Sets for Transient Levy Processes with Bounded Kernels." Ann. Probab. 13 (4) 1204 - 1218, November, 1985.


Published: November, 1985
First available in Project Euclid: 19 April 2007

zbMATH: 0579.60073
MathSciNet: MR806218
Digital Object Identifier: 10.1214/aop/1176992805

Primary: 60J30
Secondary: 60G17 , 60J45 , 60K05

Keywords: ‎kernel‎ , Levy measure , potential measure , Recurrent set , Subordinators , transient process

Rights: Copyright © 1985 Institute of Mathematical Statistics

Vol.13 • No. 4 • November, 1985
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