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.
Publié le : 1985-11-14
Classification:
Recurrent set,
transient process,
kernel,
potential measure,
subordinators,
Levy measure,
60J30,
60G17,
60J45,
60K05
@article{1176992805,
author = {Janke, Steven J.},
title = {Recurrent Sets for Transient Levy Processes with Bounded Kernels},
journal = {Ann. Probab.},
volume = {13},
number = {4},
year = {1985},
pages = { 1204-1218},
language = {en},
url = {http://dml.mathdoc.fr/item/1176992805}
}
Janke, Steven J. Recurrent Sets for Transient Levy Processes with Bounded Kernels. Ann. Probab., Tome 13 (1985) no. 4, pp. 1204-1218. http://gdmltest.u-ga.fr/item/1176992805/