TY - JOUR
T1 - Two-Step Scheme for Backward Stochastic Differential Equations
AU - Han , Qiang
AU - Ji , Shaolin
JO - Journal of Computational Mathematics
VL - 2
SP - 287
EP - 304
PY - 2022
DA - 2022/11
SN - 41
DO - http://doi.org/10.4208/jcm.2112-m2019-0289
UR - https://global-sci.org/intro/article_detail/jcm/21181.html
KW - Backward stochastic differential equation, Stochastic linear two-step scheme, Local truncation error, Stability and convergence.
AB - <p style="text-align: justify;">In this paper, a stochastic linear two-step scheme has been presented to approximate backward stochastic differential equations (BSDEs). A necessary and sufficient condition is given to judge the $\mathbb{L}_2$-stability of our numerical schemes. This stochastic linear two-step method possesses a family of $3$-order convergence schemes in the sense of strong stability. The coefficients in the numerical methods are inferred based on the constraints of strong stability and $n$-order accuracy ($n\in\mathbb{N}^+$). Numerical experiments illustrate that the scheme is an efficient probabilistic numerical method.</p>