Yue Tian, Ting Wang
In this paper, inspired by the published work (Hiroshima Math. J. 54(2) (2024), pp. 219–232), we continue to explore the exponential instability of stochastic dynamical systems described by cocycles on Banach spaces. From the perspectives of both continuous time and discrete time, new Datko-type conditions for the cocycles satisfying uniform exponential instability in mean are obtained respectively.