@Article{JNMA-1-367,
author = {Li , Guangjie and Yang , Qigui},
title = {Stability Analysis for the Numerical Simulation of Hybrid Stochastic Differential Equations},
journal = {Journal of Nonlinear Modeling and Analysis},
year = {2021},
volume = {1},
number = {3},
pages = {367--383},
abstract = {<p style="text-align: justify;">This paper is mainly concerned with the exponential stability of
a class of hybrid stochastic differential equations–stochastic differential equations with Markovian switching (SDEwMSs). It first devotes to revealing that
under the global Lipschitz condition, a SDEwMS is $p$th ($p ∈ (0, 1)$) moment exponentially stable if and only if its corresponding improved Euler-Maruyama (IEM) method is $p$th moment exponentially stable for a suitable
step size. It then shows that the SDEwMS is $p$th ($p ∈ (0, 1)$) moment exponentially stable or its corresponding IEM method with small enough step sizes
implies the equation is almost surely exponentially stable or the corresponding
IEM method, respectively. In that sense, one can infer that the SDEwMS is
almost surely exponentially stable and the IEM method, no matter whether
the SDEwMS is&nbsp; $p$th moment exponentially stable or the IEM method. An
example is demonstrated to illustrate the obtained results.</p>},
issn = {2562-2862},
doi = {https://doi.org/10.12150/jnma.2019.367},
url = {http://global-sci.org/intro/article_detail/jnma/18849.html}
}