# 【学术报告】2018年7月12日下午毛学荣教授来我院举办学术讲座

2018-07-11 16:38:22    浏览次数:

where $x_t=\{x(t+u):-\tau\le u\le 0\}$ is a $C([-\tau,0];\RR^n)$-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 $\tau^*$ such that the SFDE is also almost surely exponentially stable as long as $\tau < \tau^*$. We also describe a method to determine $\tau^*$ which can be computed numerically in practice.