Continuous procedure of stochastic approximation in a semi-Markov medium

• Date: 2004
• Main Authors: Chabanyuk, Ya. M., Чабанюк, Я. М.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3792
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation $$du(t)=a(t)[C(u(t),x(t))dt+σ(u(t))dw(t)]$$ in a random semi-Markov medium described by an ergodic semi-Markov process $x(t)$.