In this paper, we are concerned with probabilistic high order numerical schemesfor Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic PDEs,it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exactsolutions admit probabilistic interpretations, i.e., the solution of a fullynonlinear parabolic PDE solves a corresponding second order forward backwardstochastic differential equation (2FBSDEs). Our numerical schemes rely onsolving those 2FBSDEs, by extending our previous results [W. Zhao, Y. Fu and T.Zhou, SIAM J. Sci. Comput., 36 (2014), pp. A1731-A1751.]. Moreover, in ournumerical schemes, one has the flexibility to choose the associated forward SDE,and a suitable choice can significantly reduce the computational complexity.Various numerical examples including the HJB equations are presented to show theeffectiveness and accuracy of the proposed numerical schemes.
