@Article{CiCP-18-1482,
author = {Tao Kong, Weidong Zhao and Tao Zhou},
title = {Probabilistic High Order Numerical Schemes for Fully Nonlinear Parabolic PDEs},
journal = {Communications in Computational Physics},
year = {2018},
volume = {18},
number = {5},
pages = {1482--1503},
abstract = {<p style="text-align: justify;">In this paper, we are concerned with probabilistic high order numerical
schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic
PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact
solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear
parabolic PDE solves a corresponding second order forward backward stochastic differential
equation (2FBSDEs). Our numerical schemes rely on solving 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 our numerical 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 the effectiveness and accuracy of the proposed numerical
schemes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.240515.280815a},
url = {http://global-sci.org/intro/article_detail/cicp/11077.html}
}