@Article{JCM-31-221,
author = {Guannan Zhang, Max Gunzburger and Weidong Zhao},
title = {A Sparse-Grid Method for Multi-Dimensional Backward Stochastic Differential Equations},
journal = {Journal of Computational Mathematics},
year = {2013},
volume = {31},
number = {3},
pages = {221--248},
abstract = {<p style="text-align: justify;">A sparse-grid method for solving multi-dimensional backward stochastic differential equations (BSDEs) based on a multi-step time discretization scheme [31] is presented. In the multi-dimensional spatial domain, i.e. the Brownian space, the conditional mathematical expectations derived from the original equation are approximated using sparse-grid Gauss-Hermite quadrature rule and (adaptive) hierarchical sparse-grid interpolation. Error estimates are proved for the proposed fully-discrete scheme for multi-dimensional BSDEs with certain types of simplified generator functions. Finally, several numerical examples are provided to illustrate the accuracy and efficiency of our scheme.</p>},
issn = {1991-7139},
doi = {https://doi.org/10.4208/jcm.1212-m4014},
url = {http://global-sci.org/intro/article_detail/jcm/9732.html}
}