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

• Datum: 2006
• Hauptverfasser: Krenevych, A. P., Stanzhitskii, A. N., Креневич, А. П., Станжицький, О. М.
• Format: Artikel
• Sprache: Ukrainisch; Englisch
• Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2006
• Online Zugang: https://umj.imath.kiev.ua/index.php/umj/article/view/3472
• Назва журналу: 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...