Forward-backward stochastic differential equations and PDE with gradient dependent second order coefficients

Abstract

Abstract.We consider a system of fully coupled forward-backward stochastic differential equations.First we generalize the results of Pardoux-Tang [7] concerning the regularity of the solutions with respect to initial conditions. Then, we prove that in some particular cases this system leads to a probabilistic representation of solutions of a second-order PDE whose second order coefficients depend on the gradient of the solution. We then give some examples in dimension 1 and dimension 2 for which the assumptions are easy to check.Mathematics Subject Classification. 60H10, 60H30.

Implementation of Image Denoising based on Backward Stochastic Differential Equations

“…In image processing one can find theoretical results [1] and some practical aspects [4,6,10,11,13,16] of BSDE-based applications. In [4] the problem of reconstruction of the noisy chromaticity is considered.…”