Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900156 | Journal of Mathematical Analysis and Applications | 2018 | 16 Pages |
Abstract
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Ping Guo, Chong-Jun Li,