# Error expansion for the discretization of Backward Stochastic Differential Equations

Abstract : We study the error induced by the time discretization of a decoupled forward-backward stochastic differential equations $(X,Y,Z)$. The forward component $X$ is the solution of a Brownian stochastic differential equation and is approximated by a Euler scheme $X^N$ with $N$ time steps. The backward component is approximated by a backward scheme. Firstly, we prove that the errors $(Y^N-Y,Z^N-Z)$ measured in the strong $L_p$-sense ($p \geq 1$) are of order $N^{-1/2}$ (this generalizes the results by Zhang 2004). Secondly, an error expansion is derived: surprisingly, the first term is proportional to $X^N-X$ while residual terms are of order $N^{-1}$.
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Article dans une revue
Stochastic Processes and their Applications, Elsevier, 2007, 117 (7), pp.803-829. 〈10.1016/j.spa.2006.10.007〉
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https://hal.archives-ouvertes.fr/hal-00019463
Contributeur : Emmanuel Gobet <>
Soumis le : mercredi 22 février 2006 - 15:08:21
Dernière modification le : jeudi 9 février 2017 - 15:08:14
Document(s) archivé(s) le : samedi 3 avril 2010 - 22:32:48

### Citation

Emmanuel Gobet, Céline Labart. Error expansion for the discretization of Backward Stochastic Differential Equations. Stochastic Processes and their Applications, Elsevier, 2007, 117 (7), pp.803-829. 〈10.1016/j.spa.2006.10.007〉. 〈hal-00019463〉

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