|
| Stability Analysis for the Numerical Simulation of Hybrid Stochastic Differential Equations |
| |
| View Full Text View/Add Comment Download reader |
| KeyWord:Moment exponential stability almost sure exponential stability Markovian switching improved Euler-Maruyama method |
| Author Name | Affiliation | | Guangjie Li | Department of Mathematics, Shenzhen Technology University, Shenzhen, Guangdong 518118, China
School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China | | Qigui Yang | School of Mathematics, South China University of Technology, Guangzhou, Guangdong 510640, China |
|
| Hits: 563 |
| Download times: 667 |
| 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 reveal that under the global Lipschitz condition, a SDEwMS is pth (p ∈ (0,1)) moment exponentially stable if and only if its corresponding improved Euler-Maruyama(IEM) method is pth moment exponentially stable for a suitable step size. It then shows that the SDEwMS is pth(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 pth moment exponentially stable or the IEM method. An example is demonstrated to illustrate the obtained results. |
|
|
|
