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Article Dans Une Revue SIAM/ASA Journal on Uncertainty Quantification Année : 2016

Empirical Regression Method for Backward Doubly Stochastic Differential Equations

Résumé

In this paper we design a numerical scheme for approximating Backward Doubly Stochastic Differential Equations (BDSDEs for short) which represent solution to Stochastic Partial Differential Equations (SPDEs). We first use a time-discretization and then, we decompose the value function on a functions basis. The functions are deterministic and depend only on time-space variables, while decomposition coefficients depend on the external Brownian motion B. The coefficients are evaluated through a empirical regression scheme, which is performed conditionally to B. We establish non asymptotic error estimates, conditionally to B, and deduce how to tune parameters to obtain a convergence conditionally and unconditionally to B. We provide numerical experiments as well.
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Dates et versions

hal-01152886 , version 1 (21-05-2015)

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Achref Bachouch, Emmanuel Gobet, Anis Matoussi. Empirical Regression Method for Backward Doubly Stochastic Differential Equations. SIAM/ASA Journal on Uncertainty Quantification, 2016, 4 (1), pp.358-379. ⟨10.1137/15M1022094⟩. ⟨hal-01152886⟩
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