Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900306 | Journal of Mathematical Analysis and Applications | 2018 | 19 Pages |
Abstract
This paper is concerned with the almost sure exponential stability of the n-dimensional nonlinear hybrid stochastic functional differential equation (SFDE) dx(t)=f(Ï1(xt,t),r(t),t)dt+g(Ï2(xt,t),r(t),t)dB(t), where xt={x(t+u):âÏâ¤uâ¤0} is a C([âÏ,0];Rn)-valued process, B(t) is an m-dimensional Brownian motion while r(t) is a Markov chain. We show that if the corresponding hybrid stochastic differential equation (SDE) dy(t)=f(y(t),r(t),t)dt+g(y(t),r(t),t)dB(t) is almost surely exponentially stable, then there exists a positive number Ïâ such that the SFDE is also almost surely exponentially stable as long as Ï<Ïâ. We also describe a method to determine Ïâ which can be computed numerically in practice.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Minghui Song, Xuerong Mao,