Comptes Rendus
Probability Theory
Comparison theorem for Brownian multidimensional BSDEs via jump processes
[Théorème de comparaison pour EDSR multidimensionnelles browniennes par processus à sauts]
Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 463-468.

Dans cette Note, nous donnons une preuve originale du théorème de comparaison pour les EDSR multidimensionnelles browniennes dans le cas où chaque ligne k du générateur ne dépend que de la k-ième ligne de lʼinconnue Z.

In this Note, we provide an original proof of the comparison theorem for multidimensional Brownian BSDEs in the case where at each line k the generator depends on the matrix variable Z only through its row k.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.03.012
Idris Kharroubi 1, 2

1 CEREMADE, CNRS, UMR 7534, université Paris Dauphine, place du Maréchal De-Lattre-De-Tassigny, 75775 Paris cedex 16, France
2 CREST, laboratoire de finance assurance, 15, boulevard Gabriel, Péri, 92245 Malakoff cedex, France
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     author = {Idris Kharroubi},
     title = {Comparison theorem for {Brownian} multidimensional {BSDEs} via jump processes},
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     pages = {463--468},
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     year = {2011},
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Idris Kharroubi. Comparison theorem for Brownian multidimensional BSDEs via jump processes. Comptes Rendus. Mathématique, Volume 349 (2011) no. 7-8, pp. 463-468. doi : 10.1016/j.crma.2011.03.012. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.012/

[1] R. Buckdahn; M. Quincampoix; A. Rascanu Viability property for a backward stochastic differential equation and applications to partial differential equations, Probab. Theory Related Fields, Volume 116 (2000), pp. 485-504

[2] Y. Hu; S. Peng On the comparison theorem for multidimensional BSDE, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 135-140

[3] S. Peng A generalized dynamic programming principle and Hamilton–Jacobi–Bellman equation, Stochastics Stochastics Rep., Volume 38 (1992), pp. 119-134

[4] M. Royer Backward stochastic differential equations with jumps and related non-linear expectation, Stochastic Proc. and their Appl., Volume 116 (2006), pp. 1358-1376

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