On the coupling property of Lévy processes

René L. Schilling; Jian Wang

Annales de l'I.H.P. Probabilités et statistiques (2011)

  • Volume: 47, Issue: 4, page 1147-1159
  • ISSN: 0246-0203

Abstract

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We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.

How to cite

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Schilling, René L., and Wang, Jian. "On the coupling property of Lévy processes." Annales de l'I.H.P. Probabilités et statistiques 47.4 (2011): 1147-1159. <http://eudml.org/doc/240107>.

@article{Schilling2011,
abstract = {We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.},
author = {Schilling, René L., Wang, Jian},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {coupling property; Lévy processes; compound Poisson processes; random walks; Mineka coupling; strong Feller property},
language = {eng},
number = {4},
pages = {1147-1159},
publisher = {Gauthier-Villars},
title = {On the coupling property of Lévy processes},
url = {http://eudml.org/doc/240107},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Schilling, René L.
AU - Wang, Jian
TI - On the coupling property of Lévy processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 2011
PB - Gauthier-Villars
VL - 47
IS - 4
SP - 1147
EP - 1159
AB - We give necessary and sufficient conditions guaranteeing that the coupling for Lévy processes (with non-degenerate jump part) is successful. Our method relies on explicit formulae for the transition semigroup of a compound Poisson process and earlier results by Mineka and Lindvall–Rogers on couplings of random walks. In particular, we obtain that a Lévy process admits a successful coupling, if it is a strong Feller process or if the Lévy (jump) measure has an absolutely continuous component.
LA - eng
KW - coupling property; Lévy processes; compound Poisson processes; random walks; Mineka coupling; strong Feller property
UR - http://eudml.org/doc/240107
ER -

References

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  12. [12] H. Thorisson. Shift-coupling in continuous time. Probab. Theory Related Fields 99 (1994) 477–483. Zbl0801.60043MR1288066
  13. [13] H. Thorisson. Coupling, Stationarity and Regeneration. Springer, New York, 2000. Zbl1044.60510MR1741181
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  15. [15] F.-Y. Wang. Functional Inequalities, Markov Processes and Spectral Theory. Science Press, Beijing, 2005. MR2127729

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