TY - JOUR
T1 - A Class of Efficient Multistep Methods for Forward Backward Stochastic Differential Equations
AU - Tang , Xiao
AU - Xiong , Jie
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 4
SP - 904
EP - 932
PY - 2024
DA - 2024/12
SN - 17
DO - http://doi.org/10.4208/nmtma.OA-2024-0010 
UR - https://global-sci.org/intro/article_detail/nmtma/23646.html
KW - Forward backward stochastic differential equations, multistep methods, efficient high-order methods, conditional expectations.
AB - <p style="text-align: justify;">A class of efficient multistep methods for forward backward stochastic differential equations (FBSDEs) are proposed and studied in this paper. According to
the characteristic of our multistep methods and replacing the corresponding Brownian motion increments with appropriate two-point distributed random variables,
we obtain a very efficient algorithm to approximate the conditional expectations
involved in the multistep methods. It is thanks to this efficient algorithm that we
can obtain a class of efficient fully discrete form of high-order methods for the FBSDEs. Finally, some numerical results are presented to illustrate the efficiency of our
multistep methods.</p>