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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Abstract

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.

Résumé

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

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

Dates
First available in Project Euclid: 6 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.aihp/1317906501

Digital Object Identifier
doi:10.1214/10-AIHP389

Mathematical Reviews number (MathSciNet)
MR2884224

Zentralblatt MATH identifier
1273.60070

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

Keywords
Stochastic equation Strong solution Pathwise uniqueness Non-Lipschitz condition

Citation

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. https://projecteuclid.org/euclid.aihp/1317906501


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References

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