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We propose a quantization-based numerical scheme for a family of decoupled FBSDEs. We simplify the scheme for the control in Pag`es and Sagna (2018) so that our approach is fully based on recursive marginal quantization and does not involve any Monte Carlo simulation for the computation of conditional expectations. We analyse in detail the numerical error of our scheme and we show through some examples the performance of the whole procedure, which proves to be very effective in view of financial applications.
We analyze the qualitative properties and the order of convergence of a splitting scheme for a class of nonlinear stochastic Schrodinger equations driven by additive It^o noise. The class of nonlinearities of interest includes nonlocal interaction cu
Relying on the classical connection between Backward Stochastic Differential Equations (BSDEs) and non-linear parabolic partial differential equations (PDEs), we propose a new probabilistic learning scheme for solving high-dimensional semi-linear par
In silico models of cardiac electromechanics couple together mathematical models describing different physics. One instance is represented by the model describing the generation of active force, coupled with the one of tissue mechanics. For the numer
We analyse a splitting integrator for the time discretization of the Schrodinger equation with nonlocal interaction cubic nonlinearity and white noise dispersion. We prove that this time integrator has order of convergence one in the $p$-th mean sens
Recently, the deep learning method has been used for solving forward-backward stochastic differential equations (FBSDEs) and parabolic partial differential equations (PDEs). It has good accuracy and performance for high-dimensional problems. In this