Almost sure exponential stability of numerical solutions for stochastic pantograph differential equations

作者：Guo, Ping; Li, Chong-Jun^*

来源：Journal of Mathematical Analysis and Applications, 2018, 460(1): 411-424.

DOI：10.1016/j.jmaa.2017.10.002

• Khasminskii-type condition
• Discrete semimartingale convergence theorem
• Almost sure exponential stability
• Euler-Maruyama method
• Backward Euler-Maruyama method

The sufficient conditions of the almost sure exponential stability of the exact solution for the stochastic pantograph differential equation are considered, with a Khasminskii-type condition. The almost sure exponential stability of the numerical solutions by the Euler-Maruyama method and the backward Euler-Maruyama method is also discussed, based on the discrete semimartingale convergence theorem. We present the sufficient conditions for the stability of the Euler-Maruyama method, with one extra condition when compared with the exact solution. We show that the backward Euler-Maruyama method can share almost the same conditions for the almost sure exponential stability as the exact solution.

• 出版日期2018-4-1
• 单位大连理工大学