Annales de l'Institut Henri Poincaré, Probabilités et Statistiques

Strong solutions for stochastic differential equations with jumps

Zenghu Li and Leonid Mytnik

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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.

Article information

Ann. Inst. H. Poincaré Probab. Statist., Volume 47, Number 4 (2011), 1055-1067.

First available in Project Euclid: 6 October 2011

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Zentralblatt MATH identifier

Primary: 60H10: Stochastic ordinary differential equations [See also 34F05] 60H20: Stochastic integral equations
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.)

Stochastic equation Strong solution Pathwise uniqueness Non-Lipschitz condition


Li, Zenghu; Mytnik, Leonid. Strong solutions for stochastic differential equations with jumps. Ann. Inst. H. Poincaré Probab. Statist. 47 (2011), no. 4, 1055--1067. doi:10.1214/10-AIHP389.

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