期刊
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS
卷 146, 期 6, 页码 1303-1328出版社
CAMBRIDGE UNIV PRESS
DOI: 10.1017/S030821051500089X
关键词
hybrid SDEs; moment exponential stability; Markov chain; Euler-Maruyama approximation; backward Euler-Maruyama approximation; split-step backward Euler-Maruyama approximation
资金
- China Postdoctoral Science Foundation [2015M571146]
- National Science Foundation of China [61473125, 11422110]
- National Natural Science Foundation of China [11371157, 91130003]
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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