Investigation of exponential dichotomy of linear Itô stochastic systems with random initial data by using quadratic forms

  • A. P. Krenevych
  • A. N. Stanzhitskii


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.
How to Cite
Krenevych, A. P., and A. N. Stanzhitskii. “Investigation of Exponential Dichotomy of Linear Itô Stochastic Systems With Random Initial Data by Using Quadratic Forms”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, no. 4, Apr. 2006, pp. 543–553,
Research articles