Almost sure exponential stability of hybrid stochastic functional differential equations

作者：Song, Minghui; Mao, Xuerong^*

来源：Journal of Mathematical Analysis and Applications, 2018, 458(2): 1390-1408.

DOI：10.1016/j.jmaa.2017.10.042

• Stability
• Hybrid stochastic differential functional equations
• Ito formula
• Brownian motion
• Markov chain

This paper is concerned with the almost sure exponential stability of the n-dimensional nonlinear hybrid stochastic functional differential equation (SFDE) dx(t) = f (psi(1) (x(t), t), r(t),t)dt + g(psi(2), t), r(t), t)dB(t), where x(t) = {x(t + u) : -tau <= u <= 0} is a C([-tau, 0]; R-n)-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 T* such that the SFDE is also almost surely exponentially stable as long as T < T*. We also describe a method to determine T* which can be computed numerically in practice.

• 出版日期2018-2-15
• 单位哈尔滨工业大学