The moment exponential stability criterion of nonlinear hybrid stochastic differential equations and its discrete approximations
Published online by Cambridge University Press: 19 July 2016
Extract
Based on the martingale theory and large deviation techniques, we investigate the pth moment exponential stability criterion of the exact and numerical solutions to hybrid stochastic differential equations (SDEs) under the local Lipschitz condition. This new stability criterion shows that Markovian switching can serve as a stochastic stabilizing factor by its logarithmic moment-generating function. We also investigate the pth moment exponential stability of Euler–Maruyama (EM), backward EM (BEM) and split-step backward EM (SSBEM) approximations for hybrid SDEs and show that, under the additional linear growth condition, the EM method can share the mean-square exponential stability of the exact solution for sufficiently small step size. However, the BEM method can work without the linear growth condition. We further investigate the SSBEM method under a coupled condition.
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- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 146 , Issue 6 , December 2016 , pp. 1303 - 1328
- Copyright
- Copyright © Royal Society of Edinburgh 2016
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