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Theses

Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs

Abstract : The purpose of this thesis is to study a numerical method for backward doubly stochastic differential equations (BDSDEs in short). In the last two decades, several methods were proposed to approximate solutions of standard backward stochastic differential equations. In this thesis, we propose an extension of one of these methods to the doubly stochastic framework. Our numerical method allows us to tackle a large class of nonlinear stochastic partial differential equations (SPDEs in short), thanks to their probabilistic interpretation. In the last part, we study a new particle method in the context of shielding studies.
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Achref Bachouch. Numerical Computations for Backward Doubly Stochastic Differential Equations and Nonlinear Stochastic PDEs. General Mathematics [math.GM]. Université du Maine, 2014. English. ⟨NNT : 2014LEMA1034⟩. ⟨tel-01299199⟩

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