Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms - Krenevych, A. P.; Stanzhitskii, A. N. (Ukrains’kyi Matematychnyi Zhurnal, 2006)
We study conditions for the mean-square exponential dichotomy of linear Itô stochastic systems. We prove that a sufficient condition for exponential dichotomy is the existence of a quadratic form whose derivative along the solutions of a system is negative definite. The converse theorem is also proved.