Hu, YaozhongNualart, DavidSong, Xiaoming2015-03-092015-03-092011-04-01Hu, Yaozhong., Nualart, David., Song, Xiaoming. "Malliavin calculus for backward stochastic differential equations and applications to numerical solutions." Ann. Appl. Probab. Volume 21, Number 6 (2011), 2379-2423. http://dx.doi.org/10.1214/11-AAP762.https://hdl.handle.net/1808/17013This is the published version, also available here: http://dx.doi.org/10.1214/11-AAP762.In this paper we study backward stochastic differential equations with general terminal value and general random generator. In particular, we do not require the terminal value be given by a forward diffusion equation. The randomness of the generator does not need to be from a forward equation, either. Motivated from applications to numerical simulations, first we obtain the Lp-Hölder continuity of the solution. Then we construct several numerical approximation schemes for backward stochastic differential equations and obtain the rate of convergence of the schemes based on the obtained Lp-Hölder continuity results. The main tool is the Malliavin calculus.Backward stochastic differential equationsMalliavin calculusexplicit schemeimplicit schemeClark–Ocone–Haussman formularate of convergenceHölder continuity of the solutionsArticle10.1214/11-AAP762openAccess