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In the present paper, we first deal with the discretization of stochastic differentialequations. We elaborate on the analysis of the weak error of the Euler scheme by Talay andTubaro 31 to contruct schemes with quicker weak rate of convergence for SDEscorresponding to an infinitesimal generator with smooth coefficients. We also extend thisanalysis to the case of a discontinuous drift coefficient. In a second part, we presenttwo applications of stochastic gradient algorithms in finance

esaim. proceedings

On two numerical problems in applied probability : discretization of Stochastic Differential Equations and optimization of an expectation depending on a parameter