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

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.

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.

DOI: 10.1214/10-AIHP389
Classification: 60H10,  60H20,  60J80
Keywords: stochastic equation, strong solution, pathwise uniqueness, non-Lipschitz condition
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Li, Zenghu; Mytnik, Leonid. Strong solutions for stochastic differential equations with jumps. Annales de l'I.H.P. Probabilités et statistiques, Volume 47 (2011) no. 4, pp. 1055-1067. doi : 10.1214/10-AIHP389. http://www.numdam.org/articles/10.1214/10-AIHP389/

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