@Article{AAMM-15-3,
author = {Xiaotong, Li and Liao, Juan and Wei, Liu and Zhuo, Xing},
title = {Convergence and Stability of an Explicit Method for Autonomous Time-Changed Stochastic Differential Equations with Super-Linear Coefficients},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2023},
volume = {15},
number = {3},
pages = {651--683},
abstract = {<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>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2021-0335},
url = {https://global-sci.com/article/72849/convergence-and-stability-of-an-explicit-method-for-autonomous-time-changed-stochastic-differential-equations-with-super-linear-coefficients}
}