$L^{p}$-Solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and $p \in{} (1,2)$

Owo, Jean-Marc

doi:10.1051/ps/2017008

L^{p}

-Solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and

p \in (1, 2)

Owo, Jean-Marc ¹

¹ Université Félix H. Boigny, Cocody, UFR de Mathématiques et Informatique, 22 BP 582 Abidjan, Côte d’Ivoire.

ESAIM: Probability and Statistics, Tome 21 (2017), pp. 168-182.

Résumé

We study backward doubly stochastic differential equations where the coefficients satisfy stochastic Lipschitz condition. We prove the existence and uniqueness of the solution in $L^{p}$ with $p \in (1, 2)$ .

Reçu le : 2015-09-04
Accepté le : 2017-03-24

MR Zbl | 1 citation dans Numdam

DOI : 10.1051/ps/2017008

Classification : 60H05, 60H20
Mots-clés : Backward doubly stochastic differential equation, stochastic Lipschitz, L^p-Solution

Affiliations des auteurs :

Owo, Jean-Marc ¹

¹ Université Félix H. Boigny, Cocody, UFR de Mathématiques et Informatique, 22 BP 582 Abidjan, Côte d’Ivoire.

@article{PS_2017__21__168_0,
     author = {Owo, Jean-Marc},
     title = {$L^{p}${-Solutions} of backward doubly stochastic differential equations with stochastic {Lipschitz} condition and $p \in{} (1,2)$},
     journal = {ESAIM: Probability and Statistics},
     pages = {168--182},
     publisher = {EDP-Sciences},
     volume = {21},
     year = {2017},
     doi = {10.1051/ps/2017008},
     mrnumber = {3716125},
     zbl = {1393.60058},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ps/2017008/}
}

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Owo, Jean-Marc. $L^{p}$-Solutions of backward doubly stochastic differential equations with stochastic Lipschitz condition and $p \in{} (1,2)$. ESAIM: Probability and Statistics, Tome 21 (2017), pp. 168-182. doi : 10.1051/ps/2017008. http://www.numdam.org/articles/10.1051/ps/2017008/

Bibliographie
Cité par

E. Pardoux and S. Peng, Backward doubly stochastic differential equations and systems of quasilinear SPDEs. Probab. Theory Related Fields. 98 (1994) 209–227. | DOI | MR | Zbl

A. Aman, $L^{p}$ -Solutions of Backward doubly stochastic differential equations with monotne coefficients. Stochastics and Dynamics 12 (2012) 1150025. | DOI | MR | Zbl

J.-M. Owo, Backward doubly stochastic differential equations with stochastic lipschitz condition. Statist. Probab. Lett. 96 (2015) 75–84. | DOI | MR | Zbl

J. Wang, Q. Ran and Q. Chen, $L^{p}$ -Solutions of BSDEs with Stochastic Lipschitz Condition. J. Appl. Math. Stochastic Anal. 2007 (2006) 1–14. | DOI | MR | Zbl

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