On the coupling property of Lévy processes
Schilling, René L. ; Wang, Jian
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011), p. 1147-1159 / Harvested from Numdam
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Nous donnons les conditions nécessaires et suffisantes pour le succès du couplage entre des processus de Lévy (avec partie de sauts non-dégénérée). Notre méthode est basée sur les formules explicites pour le semigroupe de transition d'un processus de Poisson composé, et les résultats de Mineka et Lindvall-Rogers sur le couplage d'une marche aléatoire. En particulier, nous montrons qu'un processus de Lévy admet un couplage, s'il est un processus fortement fellerien ou si la mesure de Lévy (mesure de sauts) possède une composante absolument continue.

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.

Publié le : 2011-01-01
DOI : https://doi.org/10.1214/10-AIHP400
Classification:  60G51,  60G50,  60J25,  60J75 
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     author = {Schilling, Ren\'e L. and Wang, Jian},
     title = {On the coupling property of L\'evy processes},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     volume = {47},
     year = {2011},
     pages = {1147-1159},
     doi = {10.1214/10-AIHP400},
     zbl = {1268.60061},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPB_2011__47_4_1147_0}
}

Schilling, René L.; Wang, Jian. On the coupling property of Lévy processes. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) pp. 1147-1159. doi : 10.1214/10-AIHP400. http://gdmltest.u-ga.fr/item/AIHPB_2011__47_4_1147_0/

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