Empirical Regression Method for Backward Doubly Stochastic Differential Equations

Abstract : 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.
Type de document :
Pré-publication, Document de travail
2015
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  • HAL Id : hal-01152886, version 1

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Achref Bachouch, Emmanuel Gobet, Anis Matoussi. Empirical Regression Method for Backward Doubly Stochastic Differential Equations. 2015. 〈hal-01152886〉

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