TY - JOUR
T1 - Convergence and Stability of an Explicit Method for Autonomous Time-Changed Stochastic Differential Equations with Super-Linear Coefficients
AU - Li , Xiaotong
AU - Liao , Juan
AU - Liu , Wei
AU - Xing , Zhuo
JO - Advances in Applied Mathematics and Mechanics
VL - 3
SP - 651
EP - 683
PY - 2023
DA - 2023/02
SN - 15
DO - http://doi.org/10.4208/aamm.OA-2021-0335
UR - https://global-sci.org/intro/article_detail/aamm/21445.html
KW - Time-changed stochastic differential equations, explicit method, super-linear coefficients, strong convergence, asymptotic stability.
AB - <p style="text-align: justify;">In this paper, numerical methods for the time-changed stochastic differential
equations of the form $$d\Upsilon(t)=a(\Upsilon(t))dt+b(\Upsilon(t))dE(t)+\sigma(\Upsilon(t))dB(E(t))$$ are investigated, where all the coefficients $a(·),$ $b(·)$ and $\sigma(·)$ are allowed to contain
some super-linearly growing terms. An explicit method is proposed by using the idea
of truncating terms that grow too fast. Strong convergence in the finite time of the proposed method is proved and the convergence rate is obtained. The proposed method
is also proved to be able to reproduce the asymptotic stability of the underlying equation in the almost sure sense. Simulations are provided to demonstrate the theoretical
results.</p>