11 research outputs found
On the discretization of backward doubly stochastic differential equations
In this paper, we are dealing with the approximation of the process (Y,Z)
solution to the backward doubly stochastic differential equation with the
forward process X . After proving the L2-regularity of Z, we use the Euler
scheme to discretize X and the Zhang approach in order to give a discretization
scheme of the process (Y,Z)
Weak error in negative Sobolev spaces for the stochastic heat equation
In this paper, we make another step in the study of weak error of the
stochastic heat equation by considering norms as functional
A regression Monte-Carlo method for Backward Doubly Stochastic Differential Equations
This paper extends the idea of E.Gobet, J.P.Lemor and X.Warin from the
setting of Backward Stochastic Differential Equations to that of Backward
Doubly Stochastic Differential equations. We propose some numerical
approximation scheme of these equations introduced by E.Pardoux and S.Peng
Density estimates for solutions to one dimensional Backward SDE's
In this paper, we derive sufficient conditions for each component of the
solution to a general backward stochastic differential equation to have a
density for which upper and lower Gaussian estimates can be obtained
Weak error expansion of the implicit Euler scheme
In this paper, we extend the Talay Tubaro theorem to the implicit Euler
scheme
No English title available
Dans la premiĂšre partie de cette thĂšse, nous obtenons lâexistence dâune densitĂ© et des estimĂ©es gaussiennes pour la solution dâune Ă©quation diffĂ©rentielle stochastique rĂ©trograde. Câest une application du calcul de Malliavin et plus particuliĂšrement dâune formule dâI. Nourdin et de F. Viens. La deuxiĂšme partie de cette thĂšse est consacrĂ©e Ă la simulation dâune Ă©quation aux dĂ©rivĂ©es partielles stochastique par une mĂ©thode probabiliste qui repose sur la reprĂ©sentation de lâĂ©quation aux dĂ©rivĂ©es partielles stochastique en terme dâĂ©quation diffĂ©rentielle doublement stochastique rĂ©trograde, introduite par E. Pardoux et S. Peng. On Ă©tend dans ce cadre les idĂ©es de F. Zhang et E. Gobet et al. sur la simulation dâune Ă©quation diffĂ©rentielle stochastique rĂ©trograde. Dans la derniĂšre partie, nous Ă©tudions lâerreur faible du schĂ©ma dâEuler implicite pour les processus de diffusion et lâĂ©quation de la chaleur stochastique. Dans le premier cas, nous Ă©tendons les rĂ©sultats de D. Talay et L. Tubaro. Dans le second cas, nous Ă©tendons les travaux de A. Debussche.No English summary available