On the solution of the problem of stochastic stability of the integral manifold by the Lyapunov’s second method

• Date: 2016
• Main Authors: Vasilina, G. K., Tleubergenov, M. I., Василина, Г. К., Тлеубергенов, М. И.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2016
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1818
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

By using the method of Lyapunov functions, we establish sufficient conditions of stability and asymptotic stability in probability for the integral manifold of the Itˆo differential equations in the presence of random perturbations from the class of processes with independent increments. Theorems on...