Strong solutions for stochastic differential equations with jumps
Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1055-1067.

Nous étudions des équations stochastiques générales avec sauts et proposons un critère qui garantit l'existence et l'unicité de solutions fortes sous des conditions de régularité de type Yamada-Watanabe. Les résultats sont appliqués à des équations stochastiques conduites par des processus de Lévy de sauts positifs.

General stochastic equations with jumps are studied. We provide criteria for the uniqueness and existence of strong solutions under non-Lipschitz conditions of Yamada-Watanabe type. The results are applied to stochastic equations driven by spectrally positive Lévy processes.

DOI : https://doi.org/10.1214/10-AIHP389
Classification : 60H10,  60H20,  60J80
Mots clés : stochastic equation, strong solution, pathwise uniqueness, non-Lipschitz condition
@article{AIHPB_2011__47_4_1055_0,
     author = {Li, Zenghu and Mytnik, Leonid},
     title = {Strong solutions for stochastic differential equations with jumps},
     journal = {Annales de l'I.H.P. Probabilit\'es et statistiques},
     pages = {1055--1067},
     publisher = {Gauthier-Villars},
     volume = {47},
     number = {4},
     year = {2011},
     doi = {10.1214/10-AIHP389},
     zbl = {1273.60070},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPB_2011__47_4_1055_0/}
}
Li, Zenghu; Mytnik, Leonid. Strong solutions for stochastic differential equations with jumps. Annales de l'I.H.P. Probabilités et statistiques, Tome 47 (2011) no. 4, pp. 1055-1067. doi : 10.1214/10-AIHP389. http://archive.numdam.org/item/AIHPB_2011__47_4_1055_0/

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