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Abstract |
Second-order fully nonlinear parabolic partial differential equations (2PDEs) are associated with second-order forward backward SDEs (2FBSDEs), including semi-linear and quasi-linear PDEs as special ones associated with forward backward SDEs. By solving the associated 2FBSDEs, in this talk, we will give a stochastic scheme for solving 2PDEs, which have applications in scientific and engineering fields, such as fluid mechanics, image processing, optimal control, etc. To demonstrate the effectiveness and high accuracy of the scheme, we test our scheme by several examples, including HJB equations as special ones. Our numerical results show that the scheme is effective, highly accurate and stable. |
