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

Summary The objective of this thesis is the study of a numerical scheme for the approximation of solutions of doubly stochastic backward differential equations (DSDEs). During the last two decades, several methods have been proposed to allow the numerical solution of standard backward stochastic differential equations. In this thesis, we propose an extension of one of these methods to the doubly stochastic case. Our numerical method allows us to attack a wide range of nonlinear stochastic partial differential equations (SPDEs). This is possible through their probabilistic representation in terms of EDDSRs. In the last part, we study a new particle method in the context of neutron protection studies.