Continuous procedure of stochastic approximation in a semi-Markov medium

Using the Lyapunov function for an averaged system, we establish conditions for the convergence of the procedure of stochastic approximation in a random semi-Markov medium described by an ergodic semi-Markov process x(t).Translated from Ukrainskyi Matematychnyi Zhurnal, Vol. 56, No. 5, pp. 713–720, May, 2004.