Year: 2019
Author: Guangjie Li, Qigui Yang
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 3 : pp. 367–383
Abstract
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 $p$th moment exponentially stable or the IEM method. An example is demonstrated to illustrate the obtained results.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.12150/jnma.2019.367
Journal of Nonlinear Modeling and Analysis, Vol. 1 (2019), Iss. 3 : pp. 367–383
Published online: 2019-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: Moment exponential stability almost sure exponential stability Markovian switching improved Euler-Maruyama method.