TY - JOUR
T1 - Modified Split-Step Theta Method for Stochastic Differential Equations Driven by Fractional Brownian Motion
AU - Zhao , Jingjun
AU - Zhou , Hao
AU - Xu , Yang
JO - Journal of Computational Mathematics
VL - 5
SP - 1226
EP - 1245
PY - 2024
DA - 2024/07
SN - 42
DO - http://doi.org/10.4208/jcm.2301-m2022-0088
UR - https://global-sci.org/intro/article_detail/jcm/23276.html
KW - Stochastic differential equation, Fractional Brownian motion, Split-step theta
method, Strong convergence, Exponential stability.
AB - <p style="text-align: justify;">For solving the stochastic differential equations driven by fractional Brownian motion,
we present the modified split-step theta method by combining truncated Euler-Maruyama
method with split-step theta method. For the problem under a locally Lipschitz condition
and a linear growth condition, we analyze the strong convergence and the exponential
stability of the proposed method. Moreover, for the stochastic delay differential equations
with locally Lipschitz drift condition and globally Lipschitz diffusion condition, we give the
order of convergence. Finally, numerical experiments are done to confirm the theoretical
conclusions.</p>