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

• Date: 2006
• Main Authors: Krenevych, A. P., Stanzhitskii, A. N., Креневич, А. П., Станжицький, О. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2006
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3472
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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 prov...