Path regularity for solutions of backward stochastic differential equations

By Jin Ma, Jianfeng Zhang. 2002

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Backward Stochastic Differential Equation, Nonlinear Expectation and Their Applications (2011, background): “There are actually very active researches on numerical analysis and calculations of BSDE, see Douglas, Ma and Protter (1996), Ma and Zhang (2002), Zhanng (2004), Bouchard and Touzi (2004), Peng and Xu (2003), Gobet, Lemor and Warin (2005), Zhao et al (2006), Delarue and Menozzi (2006).”
Weak Solutions of Forward–Backward SDE's (2003, background): “[16] and Ref.”
Discrete time approximation of decoupled Forward-Backward SDE with jumps (2008, background): “Under Lipschitz continuity conditions on the coecients, Zhang [ 27 ] was able to prove that the later is of order of n 1. This remarkable result allows to derive the bound Errn(Y,Z) Cn 1/2, i.e.”
Backward SDEs with constrained jumps and quasi-variational inequalities (2008, background): “Now by Meyer and Zheng [16] (or see [15]), there exists a subsequence (Ynk)jc and a c?dl?g process Y such that (YUk)k converges to Y in distribution.”
Malliavin calculus for backward stochastic differential equations and application to numerical solutions (2011, background): “In this sense our framework extends that of [13] and is also natural.”
A regression-based Monte Carlo method to solve backward stochastic differential equations (2005, background): “The mathematical analysis of BSDE is now well understood (see [23] for recent references) and its numerical resolution has made recent progresses.”