no. 4
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 : 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/articles/10.1214/10-AIHP389/}
}
TY  - JOUR
AU  - Li, Zenghu
AU  - Mytnik, Leonid
TI  - Strong solutions for stochastic differential equations with jumps
JO  - Annales de l'I.H.P. Probabilités et statistiques
PY  - 2011
SP  - 1055
EP  - 1067
VL  - 47
IS  - 4
PB  - Gauthier-Villars
UR  - http://archive.numdam.org/articles/10.1214/10-AIHP389/
DO  - 10.1214/10-AIHP389
LA  - en
ID  - AIHPB_2011__47_4_1055_0
ER  - 
%0 Journal Article
%A Li, Zenghu
%A Mytnik, Leonid
%T Strong solutions for stochastic differential equations with jumps
%J Annales de l'I.H.P. Probabilités et statistiques
%D 2011
%P 1055-1067
%V 47
%N 4
%I Gauthier-Villars
%U http://archive.numdam.org/articles/10.1214/10-AIHP389/
%R 10.1214/10-AIHP389
%G en
%F 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/articles/10.1214/10-AIHP389/

[1] M. T. Barlow. One-dimensional stochastic differential equations with no strong solution. J. London Math. Soc. (2) 26 (1982) 335-347. | MR | Zbl

[2] R. F. Bass. Stochastic differential equations driven by symmetric stable processes. In Séminaire de Probabilités, XXXVI. Lecture Notes in Math. 1801 302-313. Springer, Berlin, 2003. | Numdam | MR | Zbl

[3] R. F. Bass, K. Burdzy and Z.-Q. Chen. Stochastic differential equations driven by stable processes for which pathwise uniqueness fails. Stochastic Process. Appl. 111 (2004) 1-15. | MR | Zbl

[4] Z. F. Fu and Z. H. Li. Stochastic equations of non-negative processes with jumps. Stochastic Process. Appl. 120 (2010) 306-330. | MR | Zbl

[5] N. Ikeda and S. Watanabe. Stochastic Differential Equations and Diffusion Processes, 2nd edition. North-Holland and Kodasha, Amsterdam and Tokyo, 1989. | MR | Zbl

[6] T. Komatsu. On the pathwise uniqueness of solutions of one-dimensional stochastic differential equations of jump type. Proc. Japan Acad. Ser. A Math. Sci. 58 (1982) 353-356. | MR | Zbl

[7] R. Situ. Theory of Stochastic Differential Equations with Jumps and Applications. Springer, Berlin, 2005. | MR | Zbl

[8] T. Yamada and S. Watanabe. On the uniqueness of solutions of stochastic differential equations. J. Math. Kyoto Univ. 11 (1971) 155-167. | MR | Zbl

Cité par Sources :